Round-Pound Arithmetic

Rounded Arithmetic is the traditional way of presenting previous year accounts. The method of showing rounded sums of vectors in which the arithmetic still “adds up” and the errors in the display of the components are bounded by twice the maximum rounding error have been well known for at least 30 years in spite of there being little or nothing in the literature and no attempt to implement this in currently available spread-sheets. This paper extends the method from vectors to accumulator trees, and suggests a heuristic algorithm for the more general accumulator graphs in which nodes accumulate into more than one accumulator. The special case of crosstabulations, in which all nodes accumulate to 2 accumulators represents is considered by both recursive and non-recursive methods.