A numeric error algebra

Wetherell recently described an algebra of error values that could be added to the ordinary arithmetic of a programming language. Along with ordinary arithmetic values, error values were included in the set of computational quantities. The error values could participate in all arithmetic operations and return meaningful results. Unfortunately, the definitions of the error values were not precise enough. Using Brown's model of computer arithmetic, we supply precise definitions for the error values, define the fundamental arithmetic operations on the new values, comment on their properties, and discuss briefly how they might be used and implemented. We also compare our model to the error handling features of the proposed IEEE floating point standard.