Round-pound Arithmetic
IAIN MACCALLUM · Software Practice and Experience · 1996
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 method in currently available spreadsheets. This paper extends the method (with proof) 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 cross-tabulations, in which all nodes accumulate to two accumulators is considered by both recursive and non-recursive methods.