Register requirements of pipelined processors

To enable concurrent instruction execution, scientific computers generally rely on pipelining, which combines with faster system clocks to achieve greater throughput. Each concurrently executing instruction requires buffer space, usually implemented as a register, to receive its result. This paper focuses on the issue of how many registers are required to achieve optimal performance in pipelined scientific computers. Four machine models are considered: single, double, and triple issue scalar machines, and vector machines with various register lengths. A model is presented that accurately relates the register requirements for optimum performance cyclically scheduled loops with tree-dependence graphs to the degree of function unit pipelining, the instruction issue bandwidth, and code properties. A method for finding upper and lower bounds on the minimum register requirements is also presented.The result of this work is a theory for assessing register requirements that can be used to reveal fundamental differences among machines within a space of architectural and implementation design choices. Some experimental data is also provided to support the theory.