Linear Sequential Arrays: Pipelining Arithmetic Data Paths

Arithmetic algorithms typically use broadcasting for the distribution of control data to all bit slices in the data path. Since routing delays grow as a function of fanout and routing distance, broadcasting delays grow as a function of precision in arithmetic implementations. Broadcasting in the critical path degrades performance and causes implementations of diiering precisions to experience diierent cycle times. We present the linear sequential array (LSA) that replaces broadcasting in iterative arithmetic data paths with a pipelining scheme. With an LSA's local routing, the critical path is independent of precision. The modular design of the LSA enables precision to be extended by simply appending modules. Combinational logic hardware requirements of the LSA are the same as that of a conventional design, but the LSA generally requires more latches for delaying the transfer of data to modules farther down the pipeline. This paper discusses the LSA for general arithmetic data paths. It provides a method to convert any iterative arithmetic data path from a broadcasting approach to an LSA scheme.