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Validated roundings of dot products by sticky accumulation

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2 Author(s)
Daumas, M. ; Lab. de l''Inf. du Parallelisme, Ecole Normale Superieure de Lyon, France ; Matula, D.W.

The dot product operation is very prevalent in scientific computation and has therefore been incorporated as a primitive operation in some languages. The implementation of the dot product operation by a sequence of IEEE standard multiplications and additions does not prevent a substantial accumulation of the round-off errors or warn the user about a catastrophic cancellation. We present the design of a double precision dot product operation employing sticky accumulation, where the final rounded result is validated by raising a new exception flag if the result incurred catastrophic cancellation. Sticky accumulation can be implemented in a pipeline or parallel environment to sustain double precision with an extended control of the error. Our design allows that, in the absence of catastrophic cancellation, one ulp accuracy is guaranteed

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Computers, IEEE Transactions on  (Volume:46 ,  Issue: 5 )