A new low-power recoding algorithm for multiplierless single/multiple constant multiplication

Optimizing the number of additions in constant coefficient multiplication is conjectured to be a NP-hard problem. In this paper, we report a new heuristic requiring an average of 29.10% and 10.61 % less additions than the standard canonical signed digit representation (CSD) and the double base number system (DBNS), respectively, for 64-bit coefficients. The maximum number of additions per coefficient is bounded by (N/4)+2, and the time-complexity of the recoding is linearly proportional to N, where N is the bit-size of the constant. These performances are achieved using a new redundant version of radix-2
⁸
recoding.