Design of a fast validated dot product operation

A double precision dot product operation is designed in which the final rounded result is validated by raising exception flags if either the result incurs catastrophic cancellation or the result is not accurate to one unit in the last place (ulp). The design guarantees one ulp accuracy in the absence of catastrophic cancellation. The user can thus obtain validated results at marginal extra cost with the ability to trap to alternative routines in those cases where the results are suspicious