VALIDATED ROUNDINGS OF DOT PRODUCTS BY STICKY ACCUMULATION

The dot product operation is very prevalent in scientific computation and has therefore been incorporated as a primitive operation in some l anguages. The implementation of the dot product operation by a sequenc e of IEEE standard multiplications and additions does not prevent a su bstantial accumulation of the round-off errors or warn the user about a catastrophic cancellation. We present the design of a double precisi on dot product operation employing sticky accumulation, where the fina l rounded result is validated by raising a new exception flag if the r esult incurred catastrophic cancellation. Sticky accumulation can be i mplemented in a pipeline or parallel environment to sustain double pre cision with an extended control of the error. Our design allows that, in the absence of catastrophic cancellation, one ulp accuracy is guara nteed.