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| 1 | This·is·pdfTeX,·Version·3.14159265-2.6-1.40.21·(TeX·Live·2020/Debian)·(preloaded·format=latex·2024.1. | 1 | This·is·pdfTeX,·Version·3.14159265-2.6-1.40.21·(TeX·Live·2020/Debian)·(preloaded·format=latex·2024.1.8)··8·JAN·2024·03:43 |
| 2 | entering·extended·mode | 2 | entering·extended·mode |
| 3 | ·restricted·\write18·enabled. | 3 | ·restricted·\write18·enabled. |
| 4 | ·%&-line·parsing·enabled. | 4 | ·%&-line·parsing·enabled. |
| 5 | **qd.tex | 5 | **qd.tex |
| 6 | (./qd.tex | 6 | (./qd.tex |
| 7 | LaTeX2e·<2020-10-01>·patch·level·4 | 7 | LaTeX2e·<2020-10-01>·patch·level·4 |
| 8 | L3·programming·layer·<2021-01-09>·xparse·<2020-03-03> | 8 | L3·programming·layer·<2021-01-09>·xparse·<2020-03-03> |
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| 1 | Library·for·Double-Double·and·Quad-Double·Arithmetic∗ | 1 | Library·for·Double-Double·and·Quad-Double·Arithmetic∗ |
| 2 | Yozo·Hida† | 2 | Yozo·Hida† |
| 3 | Xiaoye·S.·Li‡ | 3 | Xiaoye·S.·Li‡ |
| 4 | David·H.·Bailey‡ | 4 | David·H.·Bailey‡ |
| 5 | January· | 5 | January·8,·2024 |
| 6 | Abstract | 6 | Abstract |
| 7 | A·double-double·number·is·an·unevaluated·sum·of·two·IEEE·double·precision·numbers, | 7 | A·double-double·number·is·an·unevaluated·sum·of·two·IEEE·double·precision·numbers, |
| 8 | capable·of·representing·at·least·106·bits·of·significand.·Similarly,·a·quad-double·number·is·an | 8 | capable·of·representing·at·least·106·bits·of·significand.·Similarly,·a·quad-double·number·is·an |
| 9 | unevaluated·sum·of·four·IEEE·double·precision·numbers,·capable·of·representing·at·least·212·bits | 9 | unevaluated·sum·of·four·IEEE·double·precision·numbers,·capable·of·representing·at·least·212·bits |
| 10 | of·significand.·Algorithms·for·various·arithmetic·operations·(including·the·four·basic·operations | 10 | of·significand.·Algorithms·for·various·arithmetic·operations·(including·the·four·basic·operations |
| 11 | and·various·algebraic·and·transcendental·operations)·are·presented.·A·C++·implementation·of | 11 | and·various·algebraic·and·transcendental·operations)·are·presented.·A·C++·implementation·of |