Accurate Arithmetic for Vector Processors

Abstract In addition to the four elementary arithmetic operations, more advanced electronic computers such as vector and parallel computers often provide a number of compound operations as additional elementary operations. If pipelined compound operations like “multiply and add,” “accumulate,” and “multiply and accumulate” contribute essentially to the high speed of the system. Accuracy requirements lead to very similar operations. We identify a set of operations which meet both requirements: high speed and accuracy. After a brief discussion of implementation techniques for the simpler of these operations we present two methods and circuits which allow a fast and correct computation of the more complicated of these operations: “accumulate” and “multiply and accumulate.” The first method computes sums and dot products by making use of a matrix-shaped and pipelined arrangement of adders which cover the full floating-point range. The second method requires some local memory on the arithmetic unit. It permits a drastic reduction in the number of adders required. Both methods can also be used to build a fast arithmetic unit for microcomputers in VLSI technology.