A distillation algorithm for floating-point summation

The addition of two or more floating-point numbers is fundamental to numeri cal computations. This paper describes an efficient "distillation" style al gorithm which produces a precise sum by exploiting the natural accuracy of compensated cancellation. The algorithm is applicable to all sets of data b ut is particularly appropriate for ill-conditioned data, where standard met hods fail due to the accumulation of rounding error and its subsequent expo sure by cancellation. The method uses only standard floating-point arithmet ic and does not rely on the radix used by the arithmetic model, the archite cture of specific machines, or the use of accumulators.