Validated roundings of dot products by sticky accumulation
| Autor: | Marc Daumas, David W. Matula |
|---|---|
| Rok vydání: | 1997 |
| Předmět: |
Sequence
Floating point Computer science Pipeline (computing) Dot product Double-precision floating-point format Theoretical Computer Science Computational Theory and Mathematics Hardware and Architecture Control theory Product (mathematics) Hardware_ARITHMETICANDLOGICSTRUCTURES Round-off error Algorithm Software |
| Zdroj: | IEEE Transactions on Computers. 46:623-629 |
| ISSN: | 0018-9340 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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