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1 This·is·pdfTeX,·Version·3.14159265-2.6-1.40.21·(TeX·Live·2020/Debian)·(preloaded·format=latex·2024.1.6)··6·JAN·2024·22:371 This·is·pdfTeX,·Version·3.14159265-2.6-1.40.21·(TeX·Live·2020/Debian)·(preloaded·format=latex·2025.2.9)··9·FEB·2025·07:10
2 entering·extended·mode2 entering·extended·mode
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6 (./qd.tex6 (./qd.tex
7 LaTeX2e·<2020-10-01>·patch·level·47 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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191 ·18033·multiletter·control·sequences·out·of·15000+600000191 ·18033·multiletter·control·sequences·out·of·15000+600000
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195 Output·written·on·qd.dvi·(24·pages,·69076·bytes).195 Output·written·on·qd.dvi·(24·pages,·69080·bytes).
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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·6,·20245 February·9,·2025
  
6 Abstract6 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·an8 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·bits9 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·operations10 of·significand.·Algorithms·for·various·arithmetic·operations·(including·the·four·basic·operations
11 and·various·algebraic·and·transcendental·operations)·are·presented.·A·C++·implementation·of11 and·various·algebraic·and·transcendental·operations)·are·presented.·A·C++·implementation·of
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