On Reducing Module Activities in Online Arithmetic Operations

Online and left-to-right arithmetic process operands and results digit-serially, most significant digit first. An online operation needs only a small number of input digits to begin producing the result digits. This property allows overlap between successive operations thus reducing data dependencies. It also enables digit-level massive parallelism and allows variable precision computations with unbiased truncation. In this paper we are exploring the property that the digits are used only when available and needed thus reducing module (signal) activities and consequently the energy consumed. We analyze a general online algorithm model and relations of input patterns on module activities in basic organizations. The two basic organizations are considered: a linear array (1D) with sequential execution, and a 2D array with combinational execution. Both organizations consist of repeated digit slices (modules). Reduction of active modules has two sources due to online mode of computation: gradual use of input digits and possibility to truncate working precision to p < n full precision. As a case study we analyze online scheme for 3D vector normalization. The results presented are analytical and the reductions in module activities are estimates. In general, the module activities are reduced by about 50% with respect to conventional arithmetic sequential and linear array implementations. Implementation is needed to obtain actual energy savings. This analysis may motivate further study of module activities as a function of arithmetic modes.