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Radix-10 BKM Algorithm for Computing Transcendentals on Pocket Computers

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(1)Radix-10 BKM Algorithm for Computing Transcendentals on Pocket Computers Laurent Imbert, Jean-Michel Muller, Fabien Rico. To cite this version: Laurent Imbert, Jean-Michel Muller, Fabien Rico. Radix-10 BKM Algorithm for Computing Transcendentals on Pocket Computers. [Research Report] RR-3754, LIP RR-1999-43, INRIA, LIP. 1999. �inria-00072908�. HAL Id: inria-00072908 https://hal.inria.fr/inria-00072908 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. Radix-10 BKM Algorithm for Computing Transcendentals on Pocket Computers Laurent Imbert , Jean-Michel Muller , Fabien Rico. No 3754 Septembre 1999 ` THEME 2. ISSN 0249-6399. apport de recherche.

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(79) 4 5,’_ 3›. %$ +/L).0Ž+ £ o4i0~#¬’o!ŒGˆo#Žonu¦}o# ~ÁˆŽ~Sgv©¨ƒªŽ˜«™¬{~]ˆJv®~]u¦}dy]¯^}Jilo±j²8³ ~]x z’ySˆJv }JiGm¶µ Î ¨g}onulJvwySulty]¯^}JiGvwtðySˆJÀ }y yS}JilonˆLˆŽ~Sgvw|#o# QYulyS}L}yƒy;x®~]ˆJz’o{º]}JilyS€Gz{*i S»JilyS€Gxw*„[oèJ}JˆŽ~]v z{i¦}¯ÛySˆJð~]ˆ»µ3Š ˆŽ~Sgv©¨@ªŽ˜«±j²8³ ~]x z’ySˆJv }JiGm |#yS€Gxw¶„[otv m¥ŒGxwonmPonuƒ}o# v uƒ}y¥Œ[y@|À’on}&|~]xw|n€Gx®~]}ySˆºG}y¥z’on}¯¿~SJ}|#ySm¥ŒGxwoC¨¶onxwonmPonu¦}Ž~]ˆJ‚­¯¹€Gul|n}JvwySulµ 13"#1<13+4/213. D ˜ HŠ4µGŠL¬ƒv #vwonuGvwÄµ^–ƒv z{ulo#@ªÙ¾&v z{v } €Gm4„[onˆ;‹&onŒGˆo#onu¦}Ž~]}JvwySu ¯¹ySˆ  ~SJ}‡è~]ˆŽ~]x xwonxRŠ;ˆJv }JiGmPon}Jvw|{;µ  /n ,n2$3$ ,0~, 5u5 3$9~,13œ36(*)lB5462nºR˜+« Zõ š ¦”¦«{«gºR˜š ˜{µ Dõp H lµ ¼ µ¦±~E‰~]ˆÁ~]ul  Dµ¦·Ùm4„[onˆJ}µ Î ¬{~]x €0~]}JvwySu-y]¯»|#ySm¥ŒGxwoC¨ÁonxwonmPonu¦}Ž~]ˆJ‚P¯Y€Gul|n}JvwySulR ZRulonÃ%¬’onˆJvwySu y]¯±j²8³Wµ ·¸u +< T,8B54T,*,7 I(+2T). , b(7 3› 73$ 5,7365 & ~,*365  8,* < V365T262-,l;.N2 y 3!B5 3$)l›5T2N,* T(*u5&5,89,12Cº ’€Gx ‚ ˜š{š{šgµR¾tonu¦¬’onˆ°ª t–@Šµ Dõ H lµ ¼ µ0±~E‰~]ˆ»º

(80) –[µ0²tx®~gº0~]ul lµå³ µl³ €Gx xwonˆµj±j²8³ ZlŠ ulonà |#ySm¥ŒGxwoC¨•~]x z’ySˆJv }JiGm ¯ÛySˆ;|#ySm¥ŒGxwoC¨ onxwonmPonu¦}Ž~]ˆJ‚P¯¹€Gul|n}JvwySulµ  /n ,n2$3$ ,n2R~, %'(*)lB5462nº¦”¦n Q SZõš{“{“ @š gºl~]€Gz{€lJ} ˜š{š]”lµ D ” H 4µ¾8~Ãvw~]ul µ³Æon‚ƒˆµ hjilo•gv!onˆonuƒ}Jv®~]x ¼½ ‹&¾t· ¼ ~]x z’ySˆJv }JiG= m Z ¼ ySulJ}Ž~]u¦}§|~]xwo§¯¿~S|Cª }ySˆdˆo#g€Gull~]u¦}v m¥ŒGxwonmPonu¦}Ž~]}JvwySu Ãv }JilyS€G}4|#ySˆJˆo#|n}Jv uGzÆv }onˆŽ~]}JvwySulµ  /1 ,n24!3$~,n2&, %'(*)lB5462nºg”¦n“ Qې SZõ{«’‘ @g˜ º

(81) ³ ~]ˆ|i7˜š{š µ Dõ“ H lµ¾ €GŒGˆŽ~]}™~]ul lµ³ µ3³•€Gx xwonˆµ hjilo ¼½ ‹;¾t· ¼ ~]x z’ySˆJv }JiG= m Z onà ˆo#J€Gx }!¯ÛySˆ!¯Û~S} `DL–@· v m¥ŒGxwonmPonu¦}Ž~]}JvwySub_µ  /n ,n2$3$ ,n2q, %'(*)+B562nºg”¦np QÛp SZ ˜ 

(82) ˜Ä‘ º  on„GˆJ€0~]ˆJ‚ ˜š{š{gµ D H³Wµ¾!µ Î ˆ|#onz’y¬{~S|j~]ul*h82µ DR~]uGzlµƒ‹;o#g€Gull~]u¦}3~]uldySugª¿x v ulo ¼½ ‹;¾t· ¼ ZŠ;ŒGŒGx vw|~]}JvwySu}ymÁ~]}JˆJv©¨ }JˆJv®~]uGz{€Gx®~]ˆJv Ä~]}JvwySuÅ~]ulÅ– ¾!µ  /1 ~,n243?,12 ~,L%'(*)+B5T2Cº<{nš Q SZö‘Sp{“ g‘E”¦«gº {€Gulo ˜š{š{«gµ DöV‘ H¥r!µ lµ onuGÀ@J}JˆŽ~gµ %  %%œ"4 UI! <_5-"$ ,*365 A).&536%'(*)+9~ ,0µl‡il¾5}Jilo#Jvwº h  ¾tonx©¯¹}º»˜š{š µ D H lµå³Wµ0³ €Gx xwonˆµ u5&5,89~ . Y)l,*3$ ,n2Cµ3±°v ˆJÀ@i ]€lonˆºb˜š{š’‘@µ Dõš H¥–[µ è~E‰ v mÁ~­h8µ»Š Ž~Sl~gº µ»hL~]À{~]z{v¿µP‹&o#g€Gull~]u¦} ¼ ySˆgvw|P³Æon}Jily@G8Ãv }JiW~ ¼ ySulJ}Ž~]uƒ}–@|~]xwo  ~S|n}ySˆ;µ  /n ,n2$3$ ,n2q, %'(*)lB5462nºG”¦n« QÛš SCºb˜š{šg˜{µ D ˜« H lµ ySxwGonˆµ3hjilo8|#ySˆgvw|8|#ySm¥ŒG€G}Jv uGzP}o#|iGuGvw†ƒ€lo{!µ  /1 ~,n243?,12A,i%'(*)+B562nº»˜š{“{šgµ D ˜{˜ H lµö–[µ £ ~]x }JilonˆµjŠ€GuGv J0o#•~]x z’ySˆJv }JiGm ¯¹ySˆ&onxwonmPonu¦}Ž~]ˆJ‚­¯¹€Gul|n}JvwySul` µ .,8U%'(*)lB54 %',?"?5 5,*365A< ?36565 ,.I2Cº<˜š’‘@˜{µ . . . . .

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(84) Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex. ´ Editeur INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France)   

(85)      ISSN 0249-6399.

(86)

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