A comparison of methods for accurate summation

Abstract

The summation of large sets of numbers is prone to serious rounding errors. Several methods of controlling these errors are compared, with respect to both speed and accuracy. It is found that the method of "Cascading Accumulators" is the fastest of several methods. The Double Compensation method (in both single and double precision versions) is also perfectly accurate in all the tests performed. Although slower than the Cascade method, it is recommended when double precision accuracy is required. C programs that implement both these methods are available in the BULLETIN online repository.