Design of a fast validated dot product operation

The dot product operation is very prevalent in sci-entiic computation and has been incorporated as a primitive operation in some languages. Implementation of the dot product operation by a sequence of IEEE standard multiplications and additions does not prevent substantial error accumulation or warn about catastrophic cancellation. The design of a double precision dot product operation is presented here where the nal rounded result is validated by raising exception ags if either the result incurred catastrophic cancellation or if the result is not accurate to one unit in the last place (ulp). Our design allows that in the absence of catastrophic cancellation one ulp accuracy is guaranteed. The user can thus obtain validated results at marginal extra cost with the facility to trap to alternative routines in those cases where the results are suspicious.