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Algorithm, Proof and Performances of a new Division of Floating Point Expansions

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(1)Algorithm, Proof and Performances of a new Division of Floating Point Expansions Marc Daumas, Claire Finot. To cite this version: Marc Daumas, Claire Finot. Algorithm, Proof and Performances of a new Division of Floating Point Expansions. [Research Report] RR-3771, INRIA. 1999. �inria-00072890�. HAL Id: inria-00072890 https://hal.inria.fr/inria-00072890 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Algorithm, Proof and Performances of a new Division of Floating Point Expansions Marc Daumas, CNRS Claire Finot, ENS de Lyon. No 3771 September 1999 ` THEME 2. ISSN 0249-6399. apport de recherche.

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(111) bdx‰qpg‘d¬®opru¯ƒ‡o|‚eKosrugnm‘’ososy}de z{eK‚ruosÄf‡¨x¨gosÄfeg@‘ z{x¨„ƒ‡‰ oswfgnx‰nbd² gÁ»qpgnzumd‡¨t{gnx‰osb4‰nruÃ>¬gnqpx‰osbdeKgopmg±’z"x¨~oszurum~m ¨opo|rv3m€x¨² b~g „g@‹xzuqptvru‡‰o¶x‰bde-zv a bdgÂx‹©»r´‘’opÆ>gn‡¨gnmGx4ezuw“bdosmdg@opmƒ¯vruqs¯ugn‘2osm\x¨b~gÂx¨g@‹xZwrumGx“z{osmz2È&G‡‰op± {o±  ¬®ru‡x‰bdg ‡‰‚x·rum~g^z{m~‘\zu’m þmGx¨gfq †x¨!b~gfgmGx¨gos±’}d~e z{m†ˆ‚os‡‰rur4m~¬®nru² ‡ºx¨bdgK‚g@wrvm~‘Ârum~gu²a bdgO‘’ru}d„~qpgOg±ƒx¨gnm~‘’g@‘ uÅ·„dopxº¬®rv‡¨ez"x3© zu}‚g@‘Âx¨rZ‚x¨ru‡‰gx‰bdgKwrueK>rumdgnmGx‰ºr{¬ õ®ö ÷€õùø.

(112) Running time (Ratio to Gaussian elimination on floating point numbers) 100000. 10000. 1000. 100. Recursive development on expansions Gaussian elimination on expansions Gaussian elimination with GMP Bareiss method on expansions Bareiss method with GMP. 10. 1 3. ³ optv}d‡‰g`"ˆŽ(gn¨}dqpx‰ rvmzum þ mGx‰gfq¾†!gfmGx¨os}de7†ˆ‡¨r©(opx¨bÂzO‡“z{m~‘’rve ez"x¨‡‰op±`² 4. 5. 6. 7. 8. 9. 10. Running time (Ratio to Gaussian elimination on floating point numbers) 100000. 10000. 1000. 100. 10. Recursive development Gaussian elimination Gaussian elimination Bareiss method Bareiss method. 1 3. ÷/÷ ñ ¸ ¹hºº ». on expansions on expansions with GMP on expansions with GMP. ³ optv}d‡‰g3›"#Ž(gn¨}dqpx‰(rvmzumRþmGx¨gnq€†!gfmGx¨os}de7†ˆ‡¨rK©(opx¨bÂzKw“bdrv¨gfmez"x‰‡¨op±¾² 4. 5. 6. 7. 8. 9. 10.

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