Free42 possible accuracy flaw
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03-30-2022, 11:51 PM
Post: #34
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RE: Free42 possible accuracy flaw
(03-30-2022 08:04 AM)Werner Wrote: 531441^1072.5 vs 9^6435 Normally, we would not expect 2 ulp error or more. (except when exponent dropped, say from 10 to 9.999...) Measure in fractions of ulp, from exact result, we expected EXP part 1/2 ulp or less, correction part of 1/2 ulp or less. Combined error almost always less than 1 full ulp. For above example, log of result gives: 14139. 14015 51585 71728 25680 61991 92905 81881 ... Here, log result had huge integer part, which kills the precision. If we had 128 good bits, (about 38 digits), say 81881 → 81900, we recovered 33 digits: 81881 → 3.5526 15792 57691 44387 92654 15646 88743 56604E+6140 81900 → 3.5526 15792 57691 44387 92654 15646 88750 31601E+6140 Even with correct recovery, EXP *then* ROUND, we were off 1 ULP. The flawed recover part added another possible ± 1 ULP |
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