Progress Report on Parallelism in MuPAD
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Progress Report on Parallelism in MuPAD Christian Heckler Torsten Metzner Paul Zimmermann. N ˚ 3154 Avril 1997 ` THEME 2. ISSN 0249-6399. apport de recherche.
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(6) . Unit´e de recherche INRIA Lorraine Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY (France) 615 rue de Jardin Botanique, BP 101, 54600 VILLERS L ES T´el´ephone : (33) 83 59 30 30 – T´el´ecopie : (33) 83 27 83 19 Antenne de Metz, technopˆole de Metz 2000, 4 rue Marconi, 55070 METZ T´el´ephone : (33) 87 20 35 00 – T´el´ecopie : (33) 87 76 39 77. "!.
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(9) ¨d dª©H ypcfsk t bdVl j t h S t `dinVhDink t VlH|8`dlni t `do8kBV^ Vl°t ¼}Vi j t i`ahDbaVH|BVD^ h t `diypj t |8Vl<V³>VW#y2baVDlUb j}l8V^ Wjz_>in`dq>k8V |8kb¢jz_8erjzefV k Y y{cgk hVl}|8Vk2³i-mrypVl|2VBy{j j:bdbEV^ bd`alW#VVDib nVD^ i¹j:ijzhink8VDbU|8VBlncg_`aW6y8b¢j:_>i¹jzin`dc:_° ºpCú·ú µ hEjzbahDk8bMc t W6Vb-²Uy{j t j:bdbV^ bd`dlnW6Vf²UWjzh S `d_8V jT W«V^ W6cf` t Vypj t ivj:eV^ Vf²HhEjzbahDk8b|2`ali t `ao2k Vf^ ² ¼}V_>i t V¼ S j t bdVl ½V t W#`dinVf² k s Y.
(10) << "}H cglniypj t jzbdbaVDb8hcfW6y8k8iV t j:bdefVo t j lncz=i- j t Vl¢lnVDVdE p=c t j t VDr`dV
(11) }j t VBV`di S V t V³>inV_2ln`dcf_8l}c:UV³>`dl-¬ i`a_2eYl m>lninVDtW# l ¢S R
(12) t j:_2| s x¼ x t=c x t i S V ¼ t%bd`ao t j t mr² s x
(13) ¼¬nX}t =c t ¼¬nX8² s t w jz_8| k8e>j o8k8l =c j:y2baVg² =c V|8k2hV ²pc lnm>linVW6lBlnypVh`¢j:bd`V|±Mc lncgW#V>`d_8|8lBc:cgy{V j¬ i`acg_8 l s ¼ =c t ba`d_8Vj t jzbdefV o t j D²Et c t cf_8bdt mic>cfbdl<=t c t |8t `dlni t `do8k8inVD|hcgS W#y8k2in`d_8t e{²Dt B`di S cgk8s ij:_>mlnm>Wo{cgbd`ah W±t j:_8`dy8t k8b¢jzin`dcf_6lnm>lniV W = ¼Mc ¼c `dlnyy cge jzW#l ° _ i Vhcg_ri j m>² k `dl jefV_2Vv¬ j:by8k ypcflnVlm>lninVDW S cflnVb¢jz_8efk{jzefVhDcf_>i¹jz`a_2lYypj t jzbdbaVDb `d_8li t k8t hin`dcg_8lln`d_8hDVi S VfV t t m opVeg`a_2t _8`d_8e ïlnV! V #">²y{jzefVl "f% $ ' &8 Bj:_8( | Ï>²}y{j:egVl® "*)'$ ' "8+ , D°%½c:}VgV ²}k8_>in`dbB_8c:~_8c%y{j j:bdbdVbBfV ln`dcg_ Bj:l.c -#h`¢j:bdbdt m t VbdVEj:lV/| ïi S Vb¢j:lifV t ln`dcf_² k s f°Ï2t ²U jzl S t VbdVEjzlnV| S =c tt lnVDqrk2Vt _>in`¢j:b}Wjzh S `a_2Vl `d_S8t VhDVWo{V RBEfS * " D²>|8k8Vincb¢j:S h c:j:hhVDlnlichcfW6S y8t k8iV l}B`di V_8cgk8e y c>hVllnc S ls j:_8|6V t -#h`dS V_>i i VEjz|8l tndt ' " ð s Vln`dinkpt j:in`dcg_#S h j:_2efV|±t `d_%S Eft* "8²g V t Vj:_®j:hDhVlnlx Bj:lBeg`atgt V_#ici V c:}V t ¼ jzb ¬ bdRBV_8S egV Sj0m S ¼} cfWi t V ¼}VS _>i V#¼ j bdVlt ½V W#`dint Vj:i S 1 - B2¬ Uc t jz`a_23V ,1Yj:_2hmr5² 4 j:_8h'V ° `dlWjzh `d_8V j:l#hDbak2lninV lB`di k8y®ic% &y c>hVllnc lVEjzh ïlnV6V 4<`defk V#' ²U`-° Vf°8`di `alV³8jzhinbdm i S Vs j t h S `dinVhDink t V±=c t S `dh SO k s Y~ t jzl|8Vl`def_8V| =c t S ¢`d_>inV S t Vlni`a_2e V_2cfk8e S ²j:ii S V#i`dW#Vi S V k Y b jz_8efkpj:efVBBj:l|8Vln`deg_8V|²>`-° Vf°fj cfk2_8|®E* &f8²zlnk8h W±j:h `d_8Vl|8`d|_8cfiVD³r`dli 7# 5° 8y6inc_8c:² y t cficf i-m>y{t Vl S j t V|> ¬-W#VW6c t m gV t l`dcf_8t lcz k s Y~V 2t sVs ypc t iV|Ocg_ i S V=cgbabdc:B`d_8e#t j t h S S `dinVhDs ink t VlEt k2_ ypj 9h d' " ò VDqrk2V_>i m>W#W6Vi 9m a n²¼}cf_>fVD³ ' ")*)¬ "#jz_8| `dbd`dhcf_\ jzy `dhl c:V ¼ S jzbdbaVD_8efVf°. 4<`defk. :5:Ö<;õ:ð¹ø. t Vf BR S V s c:}V t ¼ S zj bdbaVD_8efV nt t j mj t h S `dinVhDink t V.
(14) BR S Vy{jzy{V t `dlc t erjz_8`V|%j:l =cfbdbdc:BlE° Vhin`dcg_P|8Vlh t `dopVli S Vhk tt V_>ilni¹jzinVc:Bi S Vl S j t VD|>¬ W6 VW#c t m®gV t l`acgt _Ocz S k s ² jz_8|Ol S c:Bt l j t Vj:bBS V³8j:W6y8t bdVB`di S i S t V s ¼} y t cgincfi-m>ypV#gV t S l`acg_° S VDc:hin`dcf`di_®BX`dbd|8bUVoplVYh `d`dW6opVy8lbdVi W#VV_>b¢j:iV_8|eg° k{j:egVBhcf_2lni k8hilYcz i V|8`dlni `do8k8inVD|gV l`dcf_²8jz_8|#eg`agVl}lncfW6V `d_>inl } 8 DE -_i S `dllVhin`dcg_²:}V t lni<|8Vlnh t `do{VBi S V}lnm>_>i¹j:³cz k s Y y{j t j:bdbdVbglni¹jzinVW6V_>inl =c t l S j t V|>¬-W#VDW#c t m W±j:h S t `d_8Vl²Ei S V_ S c:%i S VlnV}lnivj:inVDW#V_>inlj t V}`aW6y8bdVWV_>inVD|²Ejz_8|ef`dgVlncgW#VHin`dW#`d_8egl8Mc t ypcfbdm>_8cgW#`¢j:b 0jzhinc ` Ejzin`dcf_° .
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(16) "!g¬ bdc>cfy8ltj:_8|%y{j t jzbabdVbo8bdcrh>lE° s j t j:bdbdVb#!g¬-bdcrcgy8lj t VV³8j:hibam%bd`fVlnVDqrk2V_>in`¢j:b}bdcrcgy8lE²HVD³rhDVy8ii S V gVm>c |%$`dllk8o8lin`dink8iV|orm'&("!(*)+)*,*)p - º{ ` - :º li¹j t i º V_8% | . 8: =µ . /21>8Eµ uz² 43 0 6ª 5M7 5ïª *µ 8» - º{ RBS V . 0 /91>8µ fVDmr}c t |V_{jzo8bdVli S Vk8lV t ic|8VhDb j t Vj:k8³>`dbd` j t mfj t `¢j:o8bdVl²f S `dh S j t VBbdcrhj:b8icVEj:h S y t c>hVlnlc t ° s j t j:bdbdVbUo8bdc>h >lj t V|8:V {_8V| jzl}=cfbdbdc:BlE . 8:*µ ;</28 . 0 /21>8Eµ uz² 43 6ª 5M7 °° 5>= 6ª 5M7 5@? *µ 8» . 2 S V t Vi S Vlni¹jzinVW6V_>inl6ª 5M7 5 = inc6t :ª 5M 5A?±j t VV³>VS hDk8inS V|`d_#y{Sj t jzDbabdµ VBpb-° *µ ;<_8/2V8 c: i S Vlt Vlnivj:inVDW#V_>inlBW±jm `dinlVb hcf_8l`dlniBc:lVq>k8V_>in`¢j:b<`d_8lni k8hi`dcf_8l²8`d_# `dh hEj:lVi V hcf_8li k8hi`dlB_8VV|8VD| µ Bp*µ ;/98 6ª 5M7 °° 5>= µ*8» 6ª 5M7 µ5 B ? RBS VDlnV±i S8t V= V#hDcf_8li t k2hinl C. 8:*µ ;/98 ² µ Bp*µ ;/98 j:_8|%y{j t jzbabdVb - º{ ¬-bdcrcgy j t V6i S V6cf_8bdm®y{j t jzbabdVb hcg_8lni t k8hDinl jfj:`db¢j:o8bdV`d_%i S V#W#`dh t c:¬-y{j t j:bdbdVb ïl S j t V| ¬0W6VW#c t m fV t ln`dcf_%cz k s Y° RBS Vm j t V ÒMÔÖ:D Õ:ËUÑÌ:Û%×nÎMÑ×ÒMÕ:Þ×nÑÒÖ:è>Î=ËUØMÒMÌ:Ú:ÍÏÞnÎUØMÎ×nÖ:ÔÔÒMá:×äÏ×ÔÎ{äÏÎMØMÑÌ:×HÔvë¹Ú:ÔDÎ=ÍÏ×äÏÔÒ{á:ØMäÏÑB×Ø=ÍÏ×ÖÎ=ØpØMÌ:Ü:×ÔÒMÎMÔ× äÏäÏ×nÚ:ä:×nÜ:ÖÒMØ=Ñ6ÍÏÔEä>ÒMÔëÛB×Ò=Î8ÎMÍÏÑDÑÖÖ>Ô}í>ÐUÎ=× Ì:E×nÚ:ÒM××ÖEÜ:ØMÍÏÔÔÒMäÔÛBäÏäÏ×Ôä8Þ-Ø=Ì:ÔDÍÏÖ:Î=Ó×Îè ÔÒM×Ü:ÒMÑEÞ×nÎMÎ=×ÕÍÏÖÔ $. ). F¢æ5:GF¢Ù.
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(35) 4 " . k8t Vinc i S V 0j:S hDi#t i S j:i#}V S j fV®s hDcf_8hVD_rS i t t jzinV|cgk t V t Uc t inl±cf_ i S S V!¢l S j t V|>¬-W#VW6c t m y{j t jzbabdVb g V ls `acg_ jz_8|t cgi V j:lnypVhilc: k t Y i V VB`dl<_8c|8`dlni `do8k8inVD|3ï`a_i V}lnV_2lnVBc:pW#Vll¹j:egVv¬-y{j:lln`d_8e k Yt gVS l`dcf_®jfj:`db¢j:o8bdVBlc0jt ° t s t S `d4h S cgjW4t Vi _>V}k8rW`dVo{BV typVcf|`d_> it cfczW 8Wj:h ic c:¬- y{°#j wj:bdjzbdh VS bd`dlnhW bdk8lnikV t Y`d_ inkhcgt _%_8ln`d`dllni=lHc c:t W#j Vln| ViHc:Yc:pj6`a_2_>|8k8VWypVo{_8V |8t Vcz_> iHt hk8bdk8_8l_8in`dV _8e l k s Y fV t _8Vbdlj:_8|W6`dh t cz¬0y{j t jzbabdVbd`dlnW`dl
(36) ¢c t hj:_#opV k8lnVD|#`d_8ln`d|8VBVDfV t m#hbdk8linV t ° RBS V k s Y b¢j:_2efk{jzeft VBy S t c:r`d|8tnVDt lBinci S V t k8lnV t t jlnypVh`¢jzbUhcf_8hDVt y8iicy t cfe t jzW `d_6i SRB`dS l}|8`dlni t `dt o8k8inVD|#V_>>` t cf_2W#V_>iE° ½ c:t VgV i VYhDk V_>ik8lV `d_>inV 0j:hDVY`dl}_8cfiBgV my2baVj:l¹t jz_>iBinck8lnVft ° V`d_riV -j:hVhcg_8ln`dlnilBc:H_8Vi fj `¢RBj:o8S bdVljzlBVDbabjzlBq>k8tVk8Vlj:_8|±y8`dypVlBopVi-VDV_®t |8` UV SV_>i hbdk8lniV l° t S t V 38© S 5&*§f£ ¢8§ =t ¨d©ªj VhDcfW#t W6cf_ incYjzbdbfhbdk8lint V lE²glnci VmhEjz_opVhDcf_8l`a|2V V|j:l<l j V|W#VDW#c t m < opVi-}VV_i V|8` UV V_>i hbdk8lniV l ¢`-° Vf°8egbacgo{j:bpfj `¢j:o8bdVl ; Mºp ; Mºp U -_®i S V t lni =c t W i S V_2Vifj t `¢j:o8bdV (#`dl t VEj:|®cgk8iE°}½ V t 'V (`dlhDcf_8l`a|2V t V|incopVjfj t `¢jzo8bdV_{jzW#V lc t `di`dlS _8cfiVfj:bdk{jz5 inV|° RBS V t Vlk8bdiczi S t V t VEj:| cfypV t jzin`dcf_%`dli S V_OVDfj:bdk{5 j:iV|°-_%i S V6lnVhDcf_8| =c W t i VS fj:bdk8VBcz `dl jzlnl`a5eg_8V|6in'c S ({°Ht ½ V Vjzerj:`d_ S (`dl}_8cfi}S Vfj:bdk{jzinVt|±j:_8| Vfj:bdk{jzinVlBj:lBk2lnk{jzb0° k `a_2ei VVDfj:bdk{j:i`dcf_±c: ²8_8ccgi V i¹jz2l ±hEjz_®h j:_8egVi V_8Vi fj `¢jzo8bdV (p°} lnl`def_8`d_8e#jfj:bdk8V ic#j_8ViBfj t `¢j:o8bdV`dlBi S V t Vú=c t Vj:_®j:icfW6`ahBcgy{V t j:i`dcf_° . F¢æ5:GF¢Ù.
(37) . cluster 3. cluster 2. writequeue("a",1,5). writequeue("a",1,7). . . . . .. queue named "a" of cluster 1. cluster 1. 4<`defk. :5:Ö<;õ:ð¹ø. t V{ k8Vk8VDl.
(38) ') wt j:h S hbdk8linV t hEj:_ S jfVjz_rm6_>k8Wo{V t c:q>k8Vk8Vl²Uj:_8| jhDbak2lninV t hj:_® t `aiV`d_®j:_>m#q>k8Vk2V3ïlnVV {egk V ¸0/Mµ B Hµ Hµ n 4/ G1> µ ½ V t V (+)81,t `alBi S VV³>y t Vt lnl`dcf_®S S `dh St B`dbdbUopVY t `dininVD_®inci S Vqrk2RBVk8S V7t (czi S Vhbdk8lniV t >° ~hbdk8lniV hEj:_ cf_8bdm VEjz|Oi V' lniVbdVW#VD_ric:`dinlq>k8Vk8Vf° V V±V³>`dlninlj±o8bdc>h>`a_2e j:_8|Oj _8cg_>¬-o8bdcrh >`d_8e t VEjz|jzhin`dcg_cg_®jq>k8Vk2Vf :µ>{
(39) » B µ Hµ n :µ>{
(40) » B µ Hµ n Mº ½ V t V (`dlHi S VB_{j:W6Vc:{i S t VBq>k8t Vk8VB i S V}s hbdk8lniV t B`dbdb t VEj:| t cfW °M {i S VBq>k8VDk8VB`dl VDS W#y8i-mi S V=k2_8hin`dcgS _ hEjzbd4b ! ,*("$ .1 ,81,Q.}B`dbab VDink _ j k cfofuvVhDiBc: i-m>ypV 18 5° -_±i VlVhcf_2|®hEj:lVi V =k2_8hRBin`dS cg_t hj:bd4b !,+("$ .1,.1,Q.BB`dbdbpo8bdcrh 6k8_>in`dbUi S V t V`dljfj:bdk8VYt jfjz`db jzo8bdVBt `d_#i S Vq>t k8VSk8Vf° V VV³>`dlninl±cg_8V®lnypVh`¢jzbq>k8Vk8V_{j:W6V | "!8+®`d_NVfV m«hbdk8linV ° B=iV i Vlnm>linVW `al `d_8`din`¢jzba` t VD|%VfV t mOhbdk8lS inV t h S Vh >l`ailq>k8Vk8V±B`di S t i S V±_{jzW#S V !8+6ty{V t `dcr|2`ahj:bdbdm S VD_P`di S j:l _8c}c inc|8S cp9° MYi V#t q>k8VDk8S V±hS cf_>i¹jz`d_8t lj:S _ V³>y VDlnln`dcg_²i `dlcg_8V#`dl VEjz|Pj:_2|%Vfj:bdk{jzinV|°S S _ V³>htVDy8in`dcf_±`dl}i V hbdk8lniV S f²> `dh _2VfV h Vh >l`din l !8+Bq>k8Vk2Vf²8o8k2ihcgW#Wk8_2`ahj:inVDl B`di i V k8lV jz_8|±S efVilivj:2l >lB`d_#i `dlB jm>° F `ai q>k8VDk8Vl}`aiH`dlypcflln`do8bdVBinclV_8|±j:_V³>y t Vlln`dcf_6incVDfV t mhbdk8linV t ²>o8k8i`di`dl_2cfiHefk{j t jz_riVV| i S j:i cf_8bdmcf_2VYhDbak2lninV t tt `dinVl S `a_6i S S Vqrk2Vk8Vczjz_8cfi S t V t hbdk8linV t ° ci S Vhbdk8t lniV t i S j:i t VEjz|8t lB t cfW `dinlq>k8Vt k8V6hEj:_2_8cft iopV# lk V6S i t jzii V#fj:bdk8VS `dlt lnVD_ri cfWt j±lnt ypVh@` {h6hbdk8lniV `diS jzS _rilic VDhVt `dfV jz_®V³>y VDlnln`dcg_® cfW° c#i V VV³>`dlnilYj:_2cfi V |{jzi¹jlni k8hik V_{jzW#V|¦ ¦8©²{ `ah `dll`aW6`db j inc q>t k8Vk2Vl t ¢lnVDV {efk t t V* ° 42c t i-}t chbdk8linV t l }j:_8t |
(41) i S V t Vt V³>`dlnilV³8j:hDt inbdm#cg_8Vy8`dypVYt cz_{j:W6V (i S j:i t k8k8_8_8l _8`d _8ecgW t cfhW bdk8lnhDibaV k2lnin V t inc±
(42) hinbdck8lhinbdV k8lni
(43) 8V °t }j y2t `aVYypi-7V }( c|8k2` _8_8V t `d_8V_>e6i y8cg`dypW VlEhD bak2lninV }inc6hbdk8lniV
(44) j:_8| j6y8`dyp7V ( ¸0 /Mµ . / . µ n
(45) 1r Hµ ½ V t VBi S VtV³>y t Vlnl`at cg_ (*)81,B`dl t `aiinVS _`aS±_ti S Vy2`aypt V ( c:8hbdk8lt inV t 5° M i S `dl t `d_8 li t k2hin`dcf_`al<y{V t =c t W#VD| o>m#hDbak2lninV >²>`diBh VEjzinVljy8`dy{V ( `dh k8_8l} cfW hbdk8linV ichbdk8lniV ° :µ>{» . / . µ 4/ :µ>{» . / . µ 4/ Mº t tYt t t i S Vy8`dyp7V (6c:hbdk8linV t r° F«`di S i S RBS VlnVhcgV _8|®hElnijzbd!bU,+`alB("$*i S &-V & o8,Qbdc>.h >hE`d_8jzebab-²Ufjj t hD` jzbak2_>lniinVcz i SVEj:V|2Mlk8_8j:h_®i`aVDcg³r_±y hEVj:lbdln4b `d!cf,*_ ( $*&-cgW RBS V=k8_2hin`dcf_ &*)*76 DV_{jzo8bdVli S Vk2lnV t c t y t cge t jzW#W6V t inc r _2&c:, .gi° S V6incgy{cgbacgefm%czi S V |8t `dli t t `do8k2inVS |6lnm>lniVW Q t &*)*76s D. t Vit k t _2lBi S V _rk2S Wo{V t czhbdk8lnS iV t lB`d_s i S V lnm>lntiVW 38&*)*76 DBF- Vink _8l#i V#_>k8WopV cz k gV _8VDbal²`-° Vf°Ui V#lk8W c:i V k Y gV _8VDbalc:`d_8|2`a>`d|8k{jzb hbdk8linV t l t 3* "& *)*s !6 D ft ² S V t V `dlBjt ypcfln`di`agVB`d_riVefV t opVi-}VV_ @jz_8| t "& *)*t 76 D#S .g² t Vik t _2lBi SS V _>k8tnWt opV cz k t Y fV _8VbdlB`d_hbdk8linV 43"{_{j:bdbdm "&+)*76 D*)81," ,"! Vink _8lBi V`d_8|8VD³czi V hk VD_rihbdk8linV ° . . . . . . . . . . . . . . F¢æ5:GF¢Ù.
(46) f cluster 3. cluster 2. writepipe("a", 1, 5). pipe named "a" running from cluster 2 to cluster 1. writepipe("a", 1, 7). . .. ... . .. ... pipe named "a" running from cluster 3 to cluster 1. cluster 1. 4<`defk 454. 687:9<;7. 4 . t V 2 s d` y{VDl. R #c `dW6y8bdVW#V_>i}i S VWjzh t cz¬0ypj t jzbdbaVDba`dlW `di `al _8VhVDlnl¹j t m%ic#i t j:_8lÃ=V t VDfV t m k s cgofuvVhi`d_ jz_ V-#hDt `aVD_r iBs jmr° 48c tt i S `al tt Vj:lncg_Pj±t o2`a_pj t t±m V_8hs c>|8`d_8e jzlh S cf lV_²S =cfbdbdc:Bt `d_8e Ï>²}f n° 1cgt inV#i S t j:i V gV s m k Y y c>hVDt|8k V`dl#j Vs egk8b¢j k Y t cfofuvt VDhiE° c%i `dl#}ct jzl|8cf_2V±=c t VDS fV m k Y cfofuvVDhiE° -_>inV _{jzbabdm±j k cfofuvVhDiY`dl Vy VlnVD_riV|Oo>m®j|2` VhiV| jzhm>hbd`dhe j:y ï`d_ lcfW#VfV t mlnRBypS Vh`¢j:b}hEj:lVl`ai`dlS j±hm>hbd`dhlni t k8hik t V' ²lt c±hcfW6W#cf_±lk8o{cgt ofuvVhill SS j t `d_8e±l S cfk8bd|S o{V jzbalc®k8lV|° `dl`dt l|8cg_8Vt `d_%S i V6cfo>>`dcfk8lBj mr°#s wfV m%cfofuvVhDi`dlWSj fVD| t B`di jtnt b jzo{VDb00° F VD_ j lnk8opcfofuúVhic>hhk lW#c Vi j:_Ocg_8hV6`a_Nj k cfofuvVDhicg_8bdm i V lic>hhDk V_8hVB`dbabo{V it t j:_2t l-=V tt V| inc±t j:_8cgi S V t hbdk8lniV t t 3<` i S S Vlnk2o{cgofuvVhi®c>s hhk t ljlVhcf_2|%in `dW#VS i S Vb jzo{VDb `dllnVD_rijzt l j Vv=V V_8hVf°½V V}Vk8lnVl`dW#`db¢j inVh _8`dq>k8Vlbd` fV df jz_8| ypV_ jzi X2 o8k2iY`d_±hcg_ri jzlni it ci S VW `di`ds l jzbalcypcflnl`do8bdVBinclnV_8|6hm>hbd`dhlni t k8hDink t Vt lE°} lBj t Vlnk8bdi²>VBt egcfiBj:_V -#h`dV_>i}V_8h c>|8`d_8S e cfW j t k cgofuvVhiinc®S j±}Vbdb ¬0|8:V {_8V|%o>m>inV6lni VEj:W czVbdVW#V_>ivj m¼ |pj:i¹j6ti-m>ypt VlE° c±i V o{jzln`dhl=c `aW6y8bdVt W#VD_ri`d_8t eBi t V hcf_2hVy8ilBc:s Yq>k8Vk8VDlj:_8®|sy8`dypVl}`a_#jzt_®V -#s h`dV_>i} jm j V s Vj:|8m>° 1 c: }VhEj:_%k2lnVj6i t j:_2lnyptc iS y cft inc>hcgt bbd` fV d ) n² a'X c inc®lV_8| k Y~cfofuvVhDinl opVi-}VV_±hS bdk8lniV l° 42c i V t lni}y cfincgi-S m>y{VBcz jt |8`dlni tt `do8k8iV| k s Yt fV t ln`dcf_ S `dh S `dW#y8bdVW6S V_>inl VS³8jzhinbdm®®i s Vb¢jz_8efk{jzefVhDcf_8li k2hinlc:i VWj:R h c:¬-y{j j:t bdbdVbd`dlnW S |2Vt lnh `do{V|%t `d_®lVt hi`acg_OS X8°df²2t V jgV h tcglnV_ S opVhEjzk8lnV `di`dlHB`a|2Vbdmjfj:`db¢j:o8bdVf° c`d_>inVDe jzinVBi Vi jz_8lnypc ib¢jmfV c:Ui V|8`dli `do8k2inV| gV l`acg_²8i Vhcf_2hVy8ic:H|8m>_{j:W6`dhBW#c>|8k8bdVl ÏX ) `dlBk8lnVD|° :5:Ö<;õ:ð¹ø.
(47) X t S S t t42c -ii}S ln`dil`dbay2b k Vt ypWcfjzl`dVf_8²Ul`dii `dVYlq>y2k8b jzVD_8ln_8in`dVcg| _ inc#c:«k2lnV_8ViBfj `¢j: o8RBbdVS lV h cfk8 vbdl|6i t o{`ao2Vk8`dinW#V| y8bd
(48) VW6Vt _>`¢j:inVo2|baVD`dl _#Ujz`d_o t V+j -#t mh'`dV _>²piB S `djh m>S ° `dlBy{j t iBc:Hi S V YXy t cEuvVhi c:Hi S V 45f"2°. Q;$9 7 G }Vln`d|8VDli S Vc t # |2Vlnh t `do{V|`d_®lnVDhin`dcf_X8°ÏX8²8jz_ j:lmr_2h S2t cf_2cfk8l cfofuvVhDic t `dV_>inV|®hDcfW#Wk2_8`dhEj:i`acg_ y t cficrhDcfb}_{j:W6V| s ss `dl|8VfS VDbacgy{VD|Pj:_2|%y{j t inbdm `dW6y8bdVWV_>S inV|<° RBS S `dly t cfinc>hcgb S jzl`d_ S V t s`dinV|Oj bdcfi c:`d|8Vsj:Ylcz jz_8|®i V81
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(83) 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) ISSN 0249-6399.
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