Using accurate arithmetics to improve numerical reproducibility and stability in parallel applications

Numerical reproducibility and stability of large scale scientific simulatio ns, especially climate modeling, on distributed memory parallel computers a re becoming critical issues. In particular, global summation of distributed arrays is most susceptible to rounding errors, and their propagation and a ccumulation cause uncertainty in final simulation results. We analyzed seve ral accurate summation methods and found that two methods are particularly effective to improve (ensure) reproducibility and stability: Kahan's self-c ompensated summation and Bailey's double-double precision summation. We pro vide an MPI operator MPI_SUMDD to work with MPI collective operations to en sure a scalable implementation on large number of processors. The final met hods are particularly simple to adopt in practical codes: not only global s ummations, but also vector-vector dot products and matrix-vector or matrix- matrix operations.