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On Ziv's rounding test
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Author | de Dinechin, Florent Lauter, Christoph Muller, Jean-Michel Torres, Serge |
| Copyright Year | 2013 |
| Abstract | A very simple test, introduced by Ziv, allows one to determine if an approximation to the value f (x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x). The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a "magic constant" e. We show how to choose that constant e to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of f (x). |
| Related Links | https://ens-lyon.hal.science/ensl-00693317v2/file/ZivRounding-final.pdf |
| ISSN | 00983500 |
| Issue Number | 4 |
| Volume Number | 39 |
| Journal | ACM Transactions on Mathematical Software |
| Language | English |
| Publisher | HAL CCSD Association for Computing Machinery |
| Publisher Date | 2013-01-01 |
| Access Restriction | Open |
| Subject Keyword | correct rounding Floating-Point arithmetic elementary functions |
| Content Type | Text |
| Resource Type | Article |
| Subject | Computer Science Software Applied Mathematics |
