Implementation and analysis of extended SLI operations

Extended arithmetic operations, such as forming scalar products, in symmetric level index (SLI) arithmetic are considered. Schemes for the implementation of such algorithms are described and analyzed in terms of comparative timings for these operations and their floating-point counterparts and in terms of the control of errors in the computation. With sufficient parallelism available in the SLI processor, the computation can be as fast as for floating-point operations. The SLI operation can be modified to produce just a single rounding error from extended operations very economically. The implementation details suggest that any time-penalty associated with the use of SLI arithmetic can be kept to a very small factor on highly parallel computers, perhaps on the order of just two or three for typical scientific computing programs.<>