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Author tim.peters
Recipients mark.dickinson, rhettinger, serhiy.storchaka, tim.peters
Date 2020-08-19.05:00:59
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Message-id <1597813259.64.0.857820021347.issue41513@roundup.psfhosted.org>
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> That's about 0.5000000000026 ulp too small - shocking ;-)

Actually, that's an illusion due to the limited precision of Decimal.  The rounded result is exactly 1/2 ulp away from the infinitely precise result - it's a nearest/even tie case.

To make analysis easy, just note that the mathematical hypot(*([x] * 9)) is exactly 3*x.  For x = 16 + ulp(16), 3*x moves to a higher binade and has two trailing one bits.  The last has to be rounded away, rounding up to leave the last retained bit even.  Any source of error, no matter how tiny, can be enough so that doesn't happen.
History
Date User Action Args
2020-08-19 05:00:59tim.peterssetrecipients: + tim.peters, rhettinger, mark.dickinson, serhiy.storchaka
2020-08-19 05:00:59tim.peterssetmessageid: <1597813259.64.0.857820021347.issue41513@roundup.psfhosted.org>
2020-08-19 05:00:59tim.peterslinkissue41513 messages
2020-08-19 05:00:59tim.peterscreate