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Validated Roundings of Dot Products by Sticky Accumulation
May 1997 (vol. 46 no. 5)
pp. 623-629

Abstract—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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Marc Daumas, David W. Matula, "Validated Roundings of Dot Products by Sticky Accumulation," IEEE Transactions on Computers, vol. 46, no. 5, pp. 623-629, May 1997, doi:10.1109/12.589241
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