Sharp ULP rounding error bound for the hypotenuse function |
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Authors: | Abraham Ziv. |
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Affiliation: | IBM Israel, Science and Technology, Matam--Advanced Technology Center, Haifa 31905, Israel |
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Abstract: | The hypotenuse function, , is sometimes included in math library packages. Assuming that it is being computed by a straightforward algorithm, in a binary floating point environment, with round to nearest rounding mode, a sharp roundoff error bound is derived, for arbitrary precision. For IEEE single precision, or higher, the bound implies that and . Numerical experiments indicate that this bound is sharp and cannot be improved. |
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Keywords: | Rounding error error analysis relative error error bound floating point ULP hypotenuse function math library |
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