Numerical precision and roundoff considerations concerning computer code migration

Code conversion between different computer platforms may not be as straightforward or as simple as some people might think. When migrating computer codes between different computers, thought must be given to the importance of numerical precision. Some applications require greater numerical precision than others. Cray architecture treats floating-point numbers and operations as double precision compared to most other platforms, many of which are based on a 32-bit architecture. In some systems, only 32-bit compilers are available, even though the hardware is 64 bit. The default floating-point representation on the Cray is 15-place accuracy, as compared to 8 places on most workstations. Some applications do not inherently require accuracy to the 15th decimal place. Examples in nuclear engineering include Monte Carlo simulations, where numerical round-off error generated in the tracking of one neutron does not propagate seriously to neutrons in succeeding generations. Other applications, particularly time-dependent simulations, are susceptible to the cumulative effects of round-off errors. In addition, multidimensional transient simulations require an iterative solution methodology, whether the simulation is of groundwater contamination, space-time nuclear kinetics, fluid flow, or chemical migration. This paper will at least partially address the concerns of numerical precision by illustrating by example what differences in precision can do to the running of a simulation