On-line algorithms for the design of pipeline architectures

This paper presents a class of algorithms, On-Line Continued Sums/Products, which are amenable for the efficient implementation by a pipeline architecture. The implementation of these algorithms provides a simple and fast method for the evaluation of several of the elementary functions; i.e., addition, subtraction, multiplication, division, logarithm, exponentiation, sine, cosine, and tangent. In addition to possessing the expected properties necessary for the efficient implementation in a pipeline architecture, the On-Line Continued Sums/Products algorithms allow for the possibility of implementing a pipeline architecture which is dynamically reconfigurable and which can process variable precision operands.