Loop nest synthesis using the polyhedral library

HAL Id: inria-00074384

https://hal.inria.fr/inria-00074384

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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.

Loop nest synthesis using the polyhedral library

Hervé Le Verge, Vincent van Dongen, Doran Wilde

To cite this version:

Hervé Le Verge, Vincent van Dongen, Doran Wilde. Loop nest synthesis using the polyhedral library.

[Research Report] RR-2288, INRIA. 1994. �inria-00074384�

ISSN 0249-6399

a p p o r t

d e r e c h e r c h e

1994

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Loop Nest Synthesis using the Polyhedral Library

Herv´e Le Verge, Vincent Van Dongen and Doran K. Wilde

N˚ 2288

May 1994

PROGRAMME 1

Architectures parall`eles, bases de donn´ees, r´eseaux et syst`emes distribu´es

021435761981;:.143=<>1@?A:BDC*EF14CG7:7HIC"J2KLCM<L14C7N HOC*PQJ2K>3HICSRTVUWBDXYPV1N%N

Z\[%]O^O[_a``bcdfe7[=g%hLikj%bFg=j%l@[mbFn.oV_4[=_qprptsb=pkbFnuVvV_InwbFn.xLbxL]Iy@yzbbFnuL[@zbFnwbF_4lL{|bj7n~}nwjFsb`bFnxIi€nwj%[wikv@lzbFn

Z[%]I‚ƒbjeZ„

…._4o@oV]I[%j7xLb[mbFg%h@b[gmh@b†y‡LˆOˆO‰I‰d Š‹_F},cFŒOŒ42d ŽoV_4^IbFn

‘’F“q”V•4’O–—e˜y@b™š`bj%h@]@xSjm]›nw}LyLj%h@bFnœi€n(pk]>]Ooy@bFnwj=n;^4ikžObyŸ_+o]4pk}>h@bFxL[_ p9xL]O`|_ i¡y*u¢j%h@b£g=]Iy>j%b={@j

xL]O`;_qiky*u7_4yVx¤j%h@bpk]L]Ooy@bFnwjwiky@^¥]O[xLb[(i€n|xLbFn%g=[~i¡vbFx/¦†§h@b,`bj%h@]@x¥i€n(vV_OnwbFx¨]Oy¤©ªl@yVg=jwik]OyVn(ikyj%h@b

«=¬«­/®†o]4pk}>h@bFxL[=_qpprikv@[_4[m}O¦

¯±°>²*³w´µM“4¶‘O–·Z]4pk}>h@bFxL[_ p¸n%g_4y@yLiky@^;o@[%]OvLpkb`

¹Dº»

¼~½ƒ¾F¿

»

¼ÀÁr½ƒÂªÃFÄ

ÅÇÆwÈÊÉ~ËÍÌkÎ@ÏFÐmÑFÒFÓmÑFÔFÕÖ%Ò=× Õ~ØOٜÑMÚYÛw×OÙwÜVÚYÛÐ\ÝÞ=ßYà=ËâáFãÉ%äå*æ/çYèWé€åêƃáäYßYÆëqÆßYÆwìœíFÆwßYìÇíqÆçDáîkÞ=ßYÈ.É%äDËâïðqÆ.ëFÆ.èÞ=áäYßFñÆ~É~ÌóòœôVõ%ö=÷õ

èìùøËÍÌÍÌVìwÞmÌÍÌâƃã=ÆúYðËâäYÆö÷=÷ôOûü%ý‹þÿFôOèÞ=áäYßYÆ~É~Ìkô>å*Émá Émë É

ŜÅÇÆwÈÊÉ~ËÍÌkÎ4Ù=ÒFÕÖqÙw×OÙÐ@Ú =×/íËâú/ÞßYà*É%ú ÉmßYäDËóÉwÌÍÌúYð4ÞßYäYÆwëäYíqÆ@úqßDËâä/ÉmúDËâìæ/ÆwúYÆ~ÉmßYìÇíýìwäDËâÞáÿý¸ÿý þ ô

ÿðFÈ Æwß=üþ.ÉmáFëÿ !øßÇÉ%áäÿ*Þ"aèç#%$&õ%÷ö'=þ"

Unit´e de recherche INRIA Rennes

IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France) T´el´ephone : (33) 99 84 71 00 – T´el´ecopie : (33) 99 84 71 71

$#% &'9

°‘° – ¢y@by@]Ol@žOb=prpkb `¥zbj%h@]xLbxLb nw}Ly>jmhêsbFnwb|xLbyLi€x@n;xLbvV]OlVgmpkbFn(bFnwjxùzbFg=[wikj%b"s_,oV_4[mjwik[9xl@y

xL]O`|_ i¡y@b(oV]4pk}ùzbFxL[wiIl@bOu*xÍl@y"xL]O`|_ i¡y@bg=]OyLj%b={@j%l@b=pÇu*bjxLbpÍ]O[xL[mb9n~l@[p¡bFn$vV]OlVgmpkbFn i¡`v@[wiIlzbbFn¦ bj%j%b

`¥zbj%h@]xLbbFn~j.vV_OnLzbb nwl@[Êp¡bFnÊ©Y]OyVg=jwik]OyVnxLbp_(vLikvLpri¡]Ij%hêsbIl@bo]4pk}ùzbFxL[wiOl@bxLbpâ«=¬«­/®¦

µV’F‘ ³%•°¥–fZ\[%]OvLpÇsb`(b xLl,oV_4[g=]Ol@[n¢xÍl@yoV]4pk}MsbFxL[%b

- .

7*'*2&;$

§h@bnwoV_4j~i_ poV]ai¡yLj]4©.žIikb™ ]a© _;pk]L]Oo¥y@bFnwj^I]>bFn2vV_Og0/+j%],j%h@b™]O[1/‹]4©32lVg0/54rŽ6™.h@]‹nwh@]4™bFx j%hV_4j

j%h@bxL]O`|_qiky‹]4©ùy@bFnwjmbFxpk]L]OoVn¢™ikj%h+_87|y@bpk]4™b[ _ayVx l@o@ob[vV]Ol@yVx@ng_ay vVbxLbFn%g=[~i¡vbFx‹iky‹j%b[%`;n]4©_

o]4pk}>h@bFxL[%]Iy*¦:9/]L]Ooy@bFnwjnw}>yLj%h@bFnœi€n¢^O[%b™]Ol@j.]a©j%h@b]4p€xLb[¢p¡]L]Ooj%[=_4yVnœ©Y]O[%`|_4j~i¡]Iy|j%h@b]I[%}4<;>ucOc=6*™.h@b[%b

ikjù™._On nwh@]4™.yj%hV_ajù_qprpVpk]>]Io|j%[=_4yVnœ©Y]O[%`|_4j~i¡]IyVng=]OlLp€x;vb.oVb[w©Y]O[%`(bFxvL}xL]4iky@^_gmhV_4y@^Ob¢]4©*vV_Onœi€n ]Oyj%h@b

l@yVxLb[wpk}Iiky@^ikyVxLb={ xL]O`|_qiky*uI©ª]apópk]4™bFxvL}|_$[%bFn%g_4y@yLiky@^?>Çob[%hV_4oVn\iky _xIi"@*b[%byLj]I[xLb[A]a©j%h@bxL]O`|_qiky*¦

9/]L]Oo·y@bFnwjn~}>yLj%h@bFnœi€ni€n2vV_OnwbFx ]Oy+j%h@bo]4pk}>h@bFxL[=_qp7n%g_4y@yLiky@^‹o@[%]OvLpkb` ™.hLi€g%h·oV]>n~bFnj%h@bo@[m]OvLpkb` ]a©

B yVxIiky@^ _nwbj]4©y@bFnwj%bFx,xL]DCOpk]L]OoVn™.hLi€gmh žIinƒi¡jbF_OgmhikyLj%b^O[_qp*o]4iky>j¢iky£_o]4pk}>h@bFxL[%]Iy*¦

e7yVg=]Ol@[mj|bj_qpǦ 4kc=67™b[%b,j%h@b B [nwj;j%]¥nw]4pkžOb‹j%h@b o]4pk}>h@bFxL[=_qpn%g_4y@yLiky@^So@[m]OvLpkb` ¦§Êh@b}SlVnwbFx_

`bjmh@]x·j%]‹g=]O`o@l@j%bjmh@bpk]L]Oo¥y@bFnwjn2™.hLi€gmh·in9vV_OnwbFx ]OyS_FE@]Ol@[wikb[1GNJ,]Oj0H/Oiky·oV_qik[%™i€nwb b=prik`ikyV_4jwik]Oy

o@[%]@g=bFxLl@[%bO¦ù§ÊhLin9`bj%h@]@x‹ikyLžO]4pkžObFnj%h@b;o@[%]I‚ƒbFg=jwik]Oy·]4©7o]4pk}>h@bFxL[m]Oy _qpk]Oy@^+_4y¥_q{Li€njm] B yVx·jmh@bpk]L]Oo

v]Ol@yVx@n¦/§h@b`|_qiky xIi"7 g=lLpkjw};in¢j%hV_4jj%h@bIE ]Ol@[wikb[(CŠ,]Oj0H/Oikyb=prik`ikyV_4jwik]Oy+`bjmh@]xg=[%bF_aj%bFn [%bFxLl@yVx@_4yLj

v]Ol@yVxbIlV_4jwik]OyVn™¢hLigmh `lVnwj¢vVbb=prik`ikyV_4j%bFx‹_q©Yj%b[%™._4[x/¦#9/bJE l@[.bj7_qpǦ4â‰86_ pn~]lVnwbj%hLi€n`bjmh@]x(©Y]O[

j%h@b=ik[Z_4yVxL]O[%b„w„.g=]O`oLirpkb[F¦

§h@b7jm[_qžOb[n%_qp@]4©_2oV]4pk}Lh@bFxL[%]OyvL}_n~bjù]4©*y@bFnwj%bFx9pk]>]IoVn.g_4yvbj%h@]Ol@^OhLjù]4©_On _$p¡b={Li€g=]O^O[_ao@hLig_ p

]O[=xLb[wiky@^+]4©j%h@bikyLj%b^Ob[o]4iky>j=n2ikySj%h@bo]4pk}>h@bFxL[%]Iy*uù™.h@b[mb _ o]4iky>jK‹i€nb={@bFg=l@j%bFx¥vb=©ª]I[%b _,oV]4ikyLj

L ir©IKNM L >OK‹o@[%bFg=bFxLbFn L pkb={>i€g=]O^O[=_4o@hLi€g_qprp¡}A¦§hLlVn^ai¡žIby›_,oV]ap¡}Lh@bFxL[%]Oy*u¸p¡]L]Oo·vV]Ol@yVx·b={@o@[%bFn%nƒi¡]IyVn

g_4y,vVbxLb[wikžObFx,vL} B yVxIiky@^j%h@bpkb={Li€g_qpù`ikyLik`l@` _4yVx`;_q{>ik`l@`š]4©ùj%h@bo]4pk}>h@bFxL[m]Oy‹iky+_^4ikžOby+nwbj

]4©xIik[%bFg=j~i¡]IyVn_4yVx±iky+j%b[%`;n.]4©ùoV_a[_4`bj%b[=n7_4yVx,]Ol@jmb[p¡]L]Oo‹ž _a[wi€_4vLpkbFn¦*eWj%bFgmh@yLiOl@b;j%]xL]|jmhLin$lVnwbFn

j%h@bZ_4[_4`bjm[wi€gù„œy>jmb^Ob[Z\[%]O^O[_a`P>ƒZ„wZ AxLbžOb=pk]OobFx;v>}QE@bF_al@j%[wikb[4SR u46ǦOZ„wZ B yVx@n j%h@bÊp¡b={Li€g=]O^O[_ao@hLig

`ikyLik`l@`†]4©Vjmh@bÊn~bj]4©@iky>j%b^Ib[oV]4ikyLjn™.hLi€g%h9póikbikyVnœi€xLb_7g=]Iy>žOb={oV]4pk}Lh@bFxL[%]Oy™¢hLigmh|xLbobyVx@npriky@bF_4[wpk}

]Oy;]Oy@b]O[ù`(]O[%boV_4[_4`bjmb[n¦OZ„wZ i€n.g_qprpkbFx;jƒ™Êig=b¢©Y]O[ùbF_Ogmh(p¡]L]Oo;iky;j%h@b.pk]L]Oo;y@bFnwjFuL]OyVg=b¢©ª]O[ j%h@b¢p¡]4™b[

_4yVx·]IyVg=b;©ª]O[j%h@b;l@o@oVb[;vV]Il@yVx/¦ù§h@b(p¡]L]Oo¥b={@o@[%bFn%nœik]OyVn(`lVnwjj%h@by·vVb b={@j%[_Ig=j%bFx+]Il@j]a©7j%h@b Z„wZ

]Ol@jmo@l@jFu*™.hLi€gmh·i€n_ OlV_InœiTGÇ_87|y@bb={@o@[%bFn%nœik]Oy·j%[%bbOu™.h@b[%b(bF_Og%h·v@[_4yVgmh in2^OlV_a[xLbFx+vL}"_,g=]OyVnwj%[_ i¡yLj

_4yVx9j%h@b.j%b[%`9i¡yV_ pVy@]xLbFn h@]4p€xb=ikj%h@b[._4y2ikyVxLb={|b={@o@[%bFn%nœik]Oy;]O[ UV>Çv]Oj%j%]I`?AM`(bF_4yLiky@^jmhV_4jj%hV_4jv@[_ayVg%h

i€n(ikyL©ªbF_InœikvLp¡bO¦§h@b‹b={jm[_Og=jwik]Oy¨]4©j%h@bpk]L]OovV]Ol@yVx b={o@[%bFnmnœik]OyVn(©ª[m]O` Z„wZ ]Ol@j%o@l@j(i€n;y@]Oj_4ySbF_On~}

o@[%]IvLp¡b`˜_ayVx[%bIlLik[%bFnoV]>n~j7o@[%]@g=bFn%nœiky@^V¦ ]4prp_a[xbj_qpǦT4S,D6nwh@]4™ h@]4™WZ„ƒZg_4y,vVblVnwbFx,j%] B yVx±pk]L]Oo

v]Ol@yVx@n_4yVx;h@]4™ Z„wZ¨]Ol@j%o@l@jg_4yvVbnœik`oLpriB bFx/¦ ùhV_a`|n(/IiW4ˆD6*[%bžIikb™7n.jmh@bZ„wZ¨`bj%h@]@x;]4© B yVxIiky@^

pk]L]Oo+vV]Il@yVx@n_ayVx‹^4ikžObFnjwik`iky@^+g=]O`oV_4[~in~]OyVnvVbjw™bby+j%h@b|Z\„ƒZ `bj%h@]@x+_4yVx‹jmh@bXE ]Ol@[wikb[1GNJ,]Oj1H/Iiky

`bjmh@]x/¦

„Çy‹j%hLi€noV_4oVb[quV™bxLbFnmg=[wikvVb|_(`bj%h@]@x,j%] nmg_4y oV_4[=_4`bj%b[wiTHbFx,oV]ap¡}Lh@bFxL[_±lVnœiky@^j%h@bo]4pk}>h@bFxL[_ p

prikv@[_4[%}Y4cZ86*™.hLi€g%h±i€n.vV_On~bFx;]Oy j%h@bg=]I`o@l@j_4jwik]Oy]a©¸j%h@bxLlV_ p[%bo@[%bFnwbyLj_4j~i¡]Iy ]4©¸_9oV]4pk}Lh@bFxL[%]Oy*¦*§h@b

o@[%]IoV]>nwbFx `bj%h@]@x‹lVnwbFn$j%h@b(póikv@[_a[%}‹©Yl@yVg=jwik]Oy\[^]D_`aTbdcIedef3`%gihjm] o@[%]I‚ƒbFg=j]Ol@j$iky@y@b[pk]L]Oo i¡yVxIi€g=bFn

ikyS_,`|_4y@y@b[nœik`irp€_4[j%],j%h@bjE@]Il@[wikb[(CŠ,]Oj1H/Iiky"b=prik`ikyV_4jwik]Oy¨`bj%h@]@x/uv@l@j™ikj%h@]Il@j^Iby@b[_4jwiky@^+_4yL}

[%bFxLl@yVx@_ay>j±i¡y@bIlV_qprikjwikbFn¦§h@b b={o@[%bFnmnœik]OyVn xLb[wikžObFx ©Y[%]O`Qj%h@b+o@[m]O‚wbFg=jwik]OyŸ_4[%b‹©Yl@[%j%h@b[[%bFxLlVg=bFx vL}

g=]OyVnƒixLb[~i¡y@^¥jmh@bYk%lmD $n'+]4©7bF_Ig%h¥b={@o@[%bFn%nœik]Oy*u_4yVx·b=prik`ikyV_4jwiky@^¥o@[%bbFnwj=_4vLprin~h@bFx g=]IyVxIi¡j~i¡]IyVn

lVnœiky@^j%h@b$pri¡v@[=_4[%}j[^]_`8aobpaT_^qir"aTsog£©Yl@yVg=jwik]Oy*¦*§hLlVnu@™b2™irpópùnwh@]4™Ÿh@]4™ j%h@bnw}LyLj%h@bFnœi€n.]a©pk]L]Oo‹y@bFnwjn

g_4yvbyLi€g=b=pk}£xL]Oy@b2lVnœiky@^|jmh@boV]4pk}Lh@bFxL[_qppóikv@[_a[%}O¦

æ*æ áutqþ=þö=ö

"#%(&'*$ )— S'*-;#

! !"$#&%(')!*+",!".-&/0 1/02,34!35 !*6435#7-8"9;:(<(3=#( !/

§hLi€nnwbFg=jwik]Oy IlLi€g1/Ipk}iky>jm[%]xLlVg=bFn$j%h@bg=]IyVg=bo@j]4©ùoV]4pk}Lh@bFxL[__4yVx,oV_4[_a`bj%b[wiTHbFxo]4pk}>h@bFxL[=_j%]h@b=pko

iky"jmh@b|l@yVxLb[n~j_4yVxIiky@^+]4©.j%h@bo]4pk}>h@bFxL[m]OySn%g_4y@yLiky@^+o@[%]IvLp¡b`,¦*eo]4pk}>h@bFxL[%]Iy·inxLb

B

y@bFx·j%]vbj%h@b

nwbj]a© o]4iky>jn9vV]Ol@yVxLbFx¨vL}›_+n~bj]4©h>}LoVb[%oLp€_4y@bFn ¦?> _Og%h¥hL}LoVb[%oLp€_4y@b,i€n|_In%nw]@gmi_aj%bFx·™ikj%h _ayS_87|y@b

iky@bOlV_ póikjw}N>OK)@BA

L

A.™.hLi€gmh›xIikžIi xLbFnnwoV_Ig=biky>j%],jw™];hV_qpr©ÇnwoV_Og=bFnC_ gmpk]>nwbFx‹hV_ pó©ÇnwoV_Og=b;™.hLi€gmh"n%_4jwi€n

B

bFn

j%h@biky@bIlV_qprikjƒ}·_4yVx+_4y+]IoVby·hV_qpr©tnwoV_Ig=b™.hLi€g%h¥xL]LbFny@]OjF¦/enw}@nwj%b`!]a©¢n~lVg%h‹iky@bIlV_qprikjwikbFnikyVxLlVg=bFn_

oV]ap¡}Lh@bFxL[%]OyDFE,G@HCJI@KA LML

™.h@b[%bNI _4yVx

L

_4[mb_g=]OyVnwj_ay>j.`;_4j%[wir{ _4yVx±žObFg=j%]O[[%bFn~oVbFg=jwikžOb=pk}O¦

O©Yj%by¨™b _a[%bikyLj%b[%bFnwj%bFx¤iky xLbFnmg=[wikvLi¡y@^_+™¢h@]4pkb©Ç_4`irpk}S]4©oV]4pk}Lh@bFxL[_PDQ>RQAu]Oy@b,oV]4pk}Lh@bFxL[%]Oy

oVb[ikyVnwj=_4yVg=b]4©j%h@boV_4[_4`bjmb[n(Q¦M§hLi€n2g_4y‹vVbxL]Oy@bv>},[%boLp€_Ogmiky@^‹žObFg=j%]O[ L _4v]4žOb™ikj%h+_4y+_87|y@b

g=]O`vLikyV_4jwik]Oy,]4©\_nwbj¢]4©¸oV_a[_4`bj%b[=n$Q*¦4S } nw]xL]4iky@^VuV™b]Ov@j=_qiky _oV_4[_4`(bj%b[wiTHbFxo]4pk}>h@bFxL[%]IyC

DQ>RQA$ETG@UCVIW@KA.XQZY L[L

™.h@b[%bWI¨_4yVxZX _a[%b.g=]OyVnwj_4yLj`|_4j%[wi€g=bFn_4yVx L i€nù_g=]OyVn~j_4yLjžObFg=jm]O[F¦4§hLi€noV_4[_a`bj%b[wiTHbFx2oV]4pk}Lh@bFxL[%]Oy

g_4y¨vVb‹[%b™.[wikj%jmbySikyj%h@b±©ª]O[m` ]4©_ y@]OydGYoV_4[=_4`bj%b[wiTHbFx¨oV]ap¡}Lh@bFxL[%]Oy i¡yj%h@b‹g=]O`vLiky@bFxŸx@_4j_·_4yVx

oV_4[_a`bj%b[.nwoV_Og=b_OnC

DQ>\QA]E G@UC_^

I `8Xacb

@

Qd A LML

DNefE G b @

Qd CgIe

b @

Qd A L[L

; hV<(3P-8"9;:(<(35#& !"Ti'4/j(&*+&kl-& !"m&9+352

§] ^Oby@b[_aj%bnwbOl@byLjwi€_qp.g=]xLb(©ª]I[]OoVb[_ajwik]OyVn_4yVx ž _4[wi€_4vLpkbFnxLbFgmp€_4[mbFx+]4žOb[o]4pk}>h@bFxL[_ u¸_(pk]L]Oo·y@bFnwj

™.hLi€gmh n%g_4yVnjmh@b7^4ikžObyo]4pk}>h@bFxL[=_qp*[%b^4ik]Oy;`lVn~jùvVb^Iby@b[_4j%bFx/¦L§h@b d!"8%$ &O ?k%'i :&()!"8n¨in

©Y]O[%`|_qprpk}nwj_4j%bFx_InC

n.ikžOby _9oV_4[_4`bjmb[wiTHbFx;oV]4pk}Lh@bFxL[_qp¸xL]O`;_qikycDQ>RQAi¡y,j%b[%`|n ]4©_oV_4[_4`(bj%b[žObFg=j%]O[$Q_4yVx_nwbj]4©(o

g=]OyVnwjm[_qiky>j=nC

DQ>RQA$ETG@UCVIW@KA.XQZY L[L

™.h@b[%bNI _4yVxKX†_4[%bg=]IyVnwj_4yLj`|_4j%[wi€g=bFn]a©\nœiTHbZoVpcq£_ayVxoVpcrš[%bFnwoVbFg=j~i¡žIb=p¡}Ou*_ayVx L i€n_g=]OyVnwj_ay>j

o#GYžObFg=j%]I[Fu

o@[%]@xLlVg=bj%h@bn~bj.]4©p¡]L]Oo,vV]Ol@yVx±b={o@[%bFnmnœik]OyVnWs&tuwvxtwuzywywy{s}|0uzv||nwlVgmhj%hV_4jÊp¡]L]Ooy@bFnwjzC

çYÿæ/ç€ý

@ t Els t uwv t

¦¦¦

@ |JEls}|5uwv |

v]xL}

™irprpžOi€nœikj.]OyVg=b_4yVx;]OyLpk};]OyVg=b_qprp*iky>jmb^Ob[.oV]ai¡yLjnÊikyj%h@bxL]O`|_qikyKDQ>\QAikypkb={Li€g=]O^O[_4o@hLi€g2]O[xLb[]4©j%h@b

b=pkb`byLjn¢]4©}@ EV> @ t uzywyzy u @ | A=¦

h@by(j_qpT/Oiky@^_4vV]Ol@j_oV_4[mjwi€g=lLp_a[pk]>]Io|ž4_4[wi€_4vLpkb @ ƒu4™b.lVn~b.j%h@b.j%b[m`iky@]4pk]O^O}?#l& !8=ij%][%b=©Yb[

j%](pk]>]IoVn.™.hLi€gmh+byVgmpk]>nwbj%h@bZ@ COpk]>]Oo*uj%hV_4j¢i€nuj%h@b2p¡]L]OoVn¢]4©ùž _a[wi€_4vLpkbFnN@u%¦+blVnwb?i& !"=

j%]([%b=©ªb[¢j%]j%h@bpk]L]OoVn.g=]OyLj_qiky@bFx;iky,j%h@bN@ COpk]>]Io*uVj%hV_ajùi€nu j%h@bpk]L]OoVn]4©ž _4[~i_avLp¡bFn @ u%¦

§h@bo@[%]OvLpkb` ]4© B yVxIiky@^2pk]>]Oo(vV]Ol@yVx@n¸in\[%b=p€_4j%bFxjm]j%h@bpriky@bF_4[ùo@[%]I^O[_4``9i¡y@^o@[m]OvLpkb` _4yVxn~hV_4[%bFn

ikjng=]O`(oLp¡b={Likjw}O¦E@]I[%j%l@yV_4j%b=pk}Ouqj%h@bFnwbo@[%]OvLpkb`|n\j%byVx2j%]vVb[%b=p€_4j~i¡žIb=p¡}nw`;_qprp>Yikyjmb[%`|n]4©Vj%h@b.xIik`byVnœik]Oy

_4yVx(yLl@`vb[]4©g=]OyVnwj%[_ i¡yLjn=AxLl@bj%]2j%h@b.©Ç_Og=j j%hV_4jpk]L]OoVnù_a[%b7y@]IjxLbboLpk}|y@bFn~j%bFx/u>_4yVx(b={V_Og=jnw]ap¡l@j~i¡]IyVn

©Y]O[.jw}LoLig_ po@[%]OvLpkb`|n.g_ay vVb$©ª]Il@yVx(i¡y,[%bF_Onw]IyV_4vLpkbjwik`bO¦

) ;#

n¢i¡žIby j%h@bxL]O`;_qiky£xLb

B

y@bFx _In C

!#"$

&%(')+*-,.!/021+%*3,.!/4*3,.!/50-1

*3,.!/"*3,.!/6106"*-,.798&:

_4yVx9j%h@b7g=]OyLj%b={@jùxL]O`|_qiky

!#"$

&%('

*3.;/%*-.7

xLbFnmg=[wikvLi¡y@^(™.hV_4ji€n/Ly@]4™.yj%]vb.j%[%l@b7_o@[~i¡]I[wiÇu

j%h@b(©Y]4prp¡]4™iky@^‹©Y]Ol@[xIi"@*b[%by>j2pk]L]Oo"y@bFn~jn2™b[mb|^Oby@b[=_4j%bFx v>}"g_ pópriky@^·j%h@b|o@[m]OoV]>n~bFx+o@[%]@g=bFxLl@[%b;©Y]Ol@[

jwik`bFn u@bF_Ogmhjwik`bn%g_ay@yLi¡y@^;j%h@bxL]O`;_qikyiky£_xIi"@*b[%byLj.]O[xLb[q¦

<

Ù=?>=A@=AB=DCFEHGJILK4ÙMILKLC6N5O

<

Ù=?>=A@=AB=DCPEQGJILKR>JILKJBRN5O

<

Ù=?>=A@=AB=SCTEHGJILKJ@RILK4Ù UR>LN5OWV

_@¦§h@bpk]>]Oo,y@bFnwjiky G itua‚ ud/ L n%g_ay]O[xLb[F¦

<

Ù=?>=A@=AB=SCPEWGJILKR>JILKJBRNXO

<

Ù=?>=A@=AB=DCFEWGJILKJ@RILKR>LU C6N)O

<

Ù=?>=A@=AB=DCPEQGJILK4ÙMILKLCZY¢ÙM[LKJ@R\J>JN]O^V

v*¦V§h@bpk]L]Oo y@bFn~jiky G%‚ud//uOiL n%g_4y]O[=xLb[F¦

< Ù=?>=A@=AB=DCFEHGJILKJ@RILKJBJULC6[_KRGJNXO

<

Ù=?>=A@=AB=DCPEQGJILKR>JILKJBY`>J[LKJ@R\_C6N]O

< Ù=?>=A@=AB=SCTEHGJILK4ÙMILKLCZYÊÙM[LKJ@R\J>JN5OaV

g4¦V§Êh@bpk]>]Ioy@bFnwj.iky G/Muq‚uLi

L

n%g_4y,]O[xLb[F¦

< Ù=?>=A@=AB=SCPEWGJILK4ÙMILKLC6NXO

<

Ù=?>=A@=AB=DCFEWGJILKJ@RILK4Ù UMBRN)O

< Ù=?>=A@=AB=DCPEQGJILKR>JILKJBY`>J[LKJ@R\qÙMN]O^V

x/¦V§h@bpk]L]Oo y@bFn~jiky GiÇud//u4‚

L

n%g_4y]O[=xLb[F¦

b . ;# 7*)%

§h@b$ik`oLpkb`by>j=_4jwik]Oy ]a©¸j%h@bo@[m]OoV]>n~bFx`bj%h@]@x(i€n.vV_InwbFx;]Oyj%h@b2oV]4pk}Lh@bFxL[_qppóikv@[_a[%}:4cZ86Ǧ

æ*æ áutqþ=þö=ö

X

X

Ei¡^Il@[%bc!CVZ\[%]O‚wbFg=jwik]OylVnœiky@^?E@]Ol@[wikb[(C@Š ]Ij1H/Oikyc>¸póik`ikyV_4j~i¡]Iy

$ /ji*+i"Z2T34!<&"$#

§hLi€n `bj%h@]@x;[%bFnwb`vLpkbFn j%h@b3E ]Ol@[wikb[(CŠ,]Oj0H/Oiky >OEŠ A`bj%h@]@x9i¡y;j%hV_4j ikjo@[%]O‚wbFg=jn\j%h@b7o]4pk}>h@bFxL[m]Oy;iky

j%h@bg_4y@]OyLi€g_qp*xIi¡[mbFg=jwik]Oy]4©/iky@y@b[pk]>]Oo;ž _a[wi€_4vLpkbFniky]O[=xLb[ùj%]2b=póik`ikyV_4jmbxLboVbyVxLbyVgmikbFn.]Iy|j%h@b`,¦>§hLlVn

vV]Il@yVx@n]Oy_pk]L]Oo_a[%b©Y]Ol@yVxikyVxLbobyVxLby>j ]4©@iky@y@b[*pk]L]Oo2i¡yVxIi€g=bFn¦¢]4™bžOb[Fuj%h@b EŠ `bj%h@]@xg=]OyVnœi€xLb[n

_qprp*oV_qik[n ]4©g=]OyVnwj%[=_qiky>jn\™.h@by B yVxIi¡y@^(j%h@b7v]Ol@yVx(]Oy|jmh@b7o@[%]I‚ƒbFg=j~i¡]Iy*¦O„Çy B ^Ol@[%bcOua©ª]O[ b={ _a`oLpkbOuOpk]4™b[

vV]Il@yVx@n L ˆ+_4yVxL _4yVx¥l@o@ob[ v]Ol@yVx@n L ˆ+_ayVx L _4[mb£_qprpg=]OyVnœi€xLb[%bFxvL}¥j%h@bEŠ `bj%h@]@x/¦ù„œy

^Oby@b[_ ptu^4ikžObyBqSg=]IyVnwj%[_qikyLjnu_On2`|_4yL} _In

|

pk]L]Oo"v]Ol@yVx@ng=]OlLp€x·vb^Oby@b[_4j%bFx£i¡y¥b=prik`ikyV_4jwiky@^¥_

nœiky@^4pkbž _4[wi€_4vLpkbOuL_4yVxj%hLi€nyLl@`vVb[^O[m] ™n*b={@oV]Oy@byLjwi€_qprpk}|™Êi¡jmhj%h@by>l@`vb[ù]4©/ž _4[wi€_4vLpkbFn¦LŠ,]>nwj]4©/j%h@bFnwb

vV]Il@yVx@n.j%l@[my]Ol@j.j%]vVb2[%bFxLl@yVx@_4yLj >Çy@]OydGYj~i¡^Ih>jA_4yVx;`lVnwj.vVbb=prik`ikyV_4j%bFx/¦*§Êh@bb=prik`ikyV_4jwik]Oy‹]4©j%h@bFnwb

[%bFxLl@yVx@_4yLj¢p¡]L]Oov]Ol@yVx@ni€n_nœik^OyLiB g_4yLj7o@[m]OvLpkb` ™.h@by,lVnœiky@^|jmh@bIEŠ!`bj%h@]@x/¦

§Êh@bùo@[%]Oo]>nwbFx$`bj%h@]@xi€n*vV_InwbFx]Oy2j%h@bxL]Il@vLp¡b.xLbFn%g=[~i¡o@j~i¡]Iyv>}Š,]Oj1H/Iiky

t

4âŒ86L™.hLi€g%h2]OyLpk}g=]OyVnœi€xLb[n

oV_qik[n ]4©g=]OyVnwjm[_qiky>j=nj%hV_4j_4[%b'$'k=iYuL_4yVx(j%h@b[%b=©Y]O[%b.y@bžOb[^Oby@b[=_4j%bFnù_ay>}[%bFxLl@yVx@_4yLjvV]Ol@yVx@n3>Yprio/Ib

L ˆ_4yVx L ˆiky+j%h@bb={V_4`oLpkbDA¦*§hLlVn¢j%h@b[%bFxLl@yVx@_4yLjvV]Ol@yVx‹b=prik`ikyV_4jwik]Oy·o@hV_Onwb]4©j%h@bJEŠ—`bj%h@]@x

i€n[%boLp€_Og=bFx·™ikj%hS_ay›_Oxq‚%_Og=byVg=}·j%bFnwj]Oy·oV_qik[n2]4© g=]OyVn~j%[_qikyLjn$i¡y¥jmh@bo@[%]OoV]LnwbFx+`(bj%h@]x/¦§hLi€njmbFnwj

i€n_Ogg=]O`(oLpói€nwh@bFx¤žOb[%}+b=7gmi¡byLjwpk}¥_On%nwl@`iky@^+jmh@b|[_q}@n_4yVx žOb[%j~ig=bFn9]4©7j%h@b;oV]4pk}Lh@bFxL[%]OyS_4[mb /Ly@]4™.y*¦

§h@b_qpk^O]O[wikj%h@` `|_ i¡yLj_qikyVn vV]Ij%hj%h@bg=]OyVnwj%[=_qiky>j_4yVxjmh@b7[_q}FžOb[%jmb={[%bo@[%bFn~by>j_ajwik]Oy|]a©_$oV]4pk}Lh@bFxL[%]Oy

_qprpk]4™iky@^ j%h@b2b`oLpk] }‹]4©ùjmh@b9_Ixq‚~_Og=byVg=},j%bFnwjF¦2bboLiky@^ j%h@bxLlV_qpù[mbo@[%bFnwbyLj_4jwik]Oy,i€n]OyLpk}©YbF_OnœikvLpkb©Y]O[

nw`|_ póp*xIik`byVnœik]OyV_qpxL]O`|_ i¡yVnnœikyVg=b_DC>o]4pk}>h@bFxL[m]Oy|™Êi¡jmhgq g=]OyVn~j%[_qikyLjn`ik^OhLjùhV_qžOb_On`|_ay>}_On !"

[_q}@n#FžOb[%j~ig=bFn u/iky¥j%h@b™]O[nwjg_OnwbO¦ +b;[%b=pk}"]Iy"j%h@b;©Ç_Og=jj%hV_4jg=]O`o@l@j_ajwik]OyV_qp7xL]O`|_qikyVnjmbyVx+j%]‹vb

[%b=p€_4jwikžOb=pk}|n~`|_qprpMo]4pk}>h@bFxL[_ >Yiky;j%b[%`|n]a©êjmh@b7xIik`byVnœik]Oy _4yVxyLl@`vVb[]4©g=]OyVnwjm[_qiky>j=n=AxLl@b7jm]j%h@b©Ç_Og=j

j%hV_4j pk]L]OoVn7_a[%by@]Oj7xLbboLpk} y@bFn~j%bFx/¦

$; $#(#&%/):(i " /(' " 2T/j*+

§h@b,prikv@[_4[%}¨©Yl@yVg=jwik]Oy [^]_`8aobdc^edef `=gih‚w]4ikyVn_¥nwbj]4©priky@bFnu[_q}nu ]O[;oV]4ikyLjnjm]›_¥xL]O`;_qiky _4yVx

o@[%]@xLlVg=bFn;j%h@b‹[%bFnwlLpkjwiky@^ xL]I`|_qikyS™ikj%hŸ_qprp[%bFxLl@yVx@_ayVgmi¡bFn±b=pri¡`9i¡yV_aj%bFx/¦.„œj;in;lVn~bFx¥ikyj%hLi€n;oV_4ob[j%]

)

úYÞÈÆwäDËâÈÆùÆwßYßYÞáqÆwÞðqúDÌÉ%äYäYßDËqðFäYÆwëäYÞ.å/íqƃßYá ËâàÞ+*É

çYÿæ/ç€ý

X

Eik^Ol@[%bˆ C@e x@xIiky@^_2priky@bjm]o@[m]O‚wbFg=j.]Ol@j7_4y;ikyVxLb={

Ei¡^Il@[%bJ,4C]O`;_qiky 4i¡`(oLpóiB g_4j~i¡]Iy

b=prik`ikyV_4j%b>Ç]I[o@[%]O‚wbFg=jù]Ol@j+A*j%h@biky@y@b[pk]>]IoikyVxIig=bFnÊ©Y[%]O`Wj%h@b.v]Ol@yVx(b={o@[%bFnmnœik]OyVn ]4©*]Ol@j%b[pk]L]OoVn¦L§hLi€n

i€n¢irprp¡lVn~j%[_4j%bFx±iky B ^Ol@[%bˆ™.h@b[mb@ i€n7_4y,]Ol@j%b[¢pk]>]Oo‹ž4_4[wi€_4vLpkb_4yVxc@ in_4y±i¡y@y@b[pk]L]Oo‹ž _4[~i_avLp¡bO¦*§]

g=]O`(o@l@j%bùj%h@b\pk]>]Oo2vV]Ol@yVx@n©Y]O[*jmh@b?@ COpk]L]Oo_On_©Yl@yVg=jwik]Oy]a©VoV_4[_4`bjmb[n/_4yVx]Ol@jmb[*pk]L]Oož4_4[wi€_4vLpkbFnu4j%h@b

iky@y@b[¢p¡]L]Oož4_4[wi€_4vLpkbFnW@ u `lVnwjvVb[mb`]4žObFx(©ª[m]O`†j%h@bxL]I`|_qiky*¦V§hLi€n i€n.xL]Oy@b2v>}(o@[%]O‚wbFg=jwiky@^j%h@b

n%g_ay xL]O`;_qiky;i¡y;j%h@bxIik[%bFg=jwik]Oy]a©êjmh@b.iky@y@b[¢p¡]L]Oo;ž _4[~i_avLp¡bFnÊ]Oy>jm]j%h@bN@ GÇ_q{Li€nuL^4ikžOiky@^ L _4yVx L _On j%h@b

pk]4™b[_4yVxl@o@ob[vV]Ol@yVx@n]4©5@ %u[mbFnwoVbFg=jwikžOb=pk}O¦O§hLi€ng_4yvb_Ogg=]I`oLprin~h@bFxlVnœiky@^7jmh@bùoV]ap¡}Lh@bFxL[_qpLprikv@[_4[%}

vL}|_Ox@xIiky@^priky@bFnG D t u# zuwywyzyL ikyj%h@bxIik[%bFg=jwik]Oy]4©¸_ póp*]4©*j%h@b¢iky@y@b[pk]>]Iož _4[wi€_4vLpkbFnG@ t u @ zuwywyzyL ¦

§h@b[%bFnwlLpkjwiky@^o]4pk}>h@bFxL[m]Oy;i€n._g=}Ipri¡yVxLb[]Oobyikyj%h@bxIik[%bFg=jwik]Oy]4©*iky@y@b[pk]L]Oo;ž _4[wi€_4vLpkbFn >w_Onùnwh@]4™.y(iky

j%h@b B ^Il@[%bDAù™.hLi€gmh£hV_Iny@]|g=]OyVnwjm[_qiky>j=niky,j%b[%`|n]a©¸j%h@biky@y@b[¢pk]>]Oo,ž _4[~i_avLp¡bFn ¦

$ ' "2T/j*+$*+2T-&9+* :

§h@b$©ªl@yVg=j~i¡]IyYn :!"k=lm*g_ pópkbFxF[^]_`8aobpaT_^qir"aTsog iky j%h@bprikv@[_4[m};inxLb B y@bFx _In ©ª]apópk]4™7nC

n.ikžOby+xL]O`|_ i¡yVn I _4yVxXuj%h@by 4i¡`(oLpóir©Y}i> IuxXANE(uV™.h@bycX E IcXu I

_4yVx;j%h@b[%bxL]LbFn¢y@]Oj.b={Lin~j7_4yL}|]Ojmh@b[7xL]O`|_qiky e WnwlVgmh j%hV_4j e gX E7I gX(¦

§h@bxL]O`|_ i¡yX i€n.g_qprpkbFx;j%h@bk%lmDY¦O§h@b nƒi¡`(oLpóir©Y};©ªl@yVg=j~i¡]Iy|j%h@b[mb=©ª]O[mb B yVx@n j%h@b¢p€_4[%^ObFnwjxL]O`|_qikynwbj

>Ç]I[nw`|_ pópkbFnwj\prin~j.]4©êg=]IyVnwj%[_qikyLjn=Aj%hV_4jFu4™.h@by(iky>jmb[nwbFg=j%bFx(™ikj%hj%h@bg=]OyLj%b={@j?X i€nbIlV_qpMjm]I! X(¦V§h@b

nœik`oLprir©Y}+]OoVb[=_4jwik]Oy‹i€nxL]Oy@bvL}£g=]I`o@l@jwiky@^ j%h@b2ikyLj%b[nwbFg=jwik]OyPI"cX _ayVx ™¢hLiópkbxL]4iky@^£nw]uV[%bFg=]I[xIiky@^

™.hLi€gmh g=]IyVnwj%[_qikyLjn]4©I _a[%b$#=[%bFxLl@yVx@_4yLj&%™Êi¡jmh[%bFnwlLpkjù]a©êjmh@bùikyLj%b[nwbFg=j~i¡]Iy*¦§Êh@b.[%bFnwlLpkjù]a©Mj%h@b7nƒi¡`(oLpóir©Y}

æ*æ áutqþ=þö=ö

]Oob[_4jwik]Oyi€nj%h@byj%h@bùxL]I`|_qikyI ™ikj%hjmh@b #=[%bFxLl@yVx@_4yLj&%.g=]OyVn~j%[_qikyLjn/[%b`]4žObFx/¦=eSnœik`oLpkb ]4©b={V_4`oLpkb\in

nwh@]4™.y2iky B ^Il@[%b,@¦4„œy|j%h@bb={V_4`oLpkbOu@xL]O`|_qikygI¤i€nùnƒi¡`(oLpóiB bFx >Ç[mbFnwlLpkjwiky@^iky|xL]I`|_qiky XA*v>}b=prik`ikyV_4jwiky@^

j%h@bjw™]g=]OyVnwj%[_ i¡yLjnjmhV_4j._4[%b[%bFxLl@yVx@_4yLj™ikj%h g=]OyLj%b={jxL]O`|_qiky X(¦

$ "$"- 35-&/j !/= *"

nœiky@^jmh@b _4v]4žOb.jw™]prikv@[_4[%}©Yl@yVg=jwik]OyVnu@_$©Yl@yVg=jwik]Oy g_ay|vb™.[wikj%j%by™¢hLigmhj_D/IbFnù_n~oVbFgmiB bFx xL]O`;_qiky

D _4yVxnwboV_a[_4j%bFn >Ç]O[©Ç_Og=j%]I[n=A2i¡j;ikyLj%]¥_4y¨i¡yLj%b[n~bFg=jwik]Oy]4©j%h@b,ikyLi¡j~i_ p9g=]OyLj%b={@j xL]O`;_qikylD‹_4yVx_

nwbIl@byVg=b]4©p¡]L]Oo‹xL]O`|_qikyVnDNtuD u yzywy#>+D E.D DNt D UywyzyAù™¢h@b[%bbF_Ogmh;p¡]L]Oo xL]O`;_qiky;in

y@]Oj_¢©ªl@yVg=jwik]Oy;]4©/iky@y@b[ p¡]L]Oo;ž _4[~i_avLp¡bFn ¦>egg=]O[xIiky@^4pk}OuLj%h@bpk]L]OoxL]O`|_qikyJDa u }AŸc.g_4y;vVb.[%bFg=l@[=nœikžOb=pk}

g=]O`o@l@jmbFx _OnC

Da xE [^]_ `aTbpao_JqiraTsog > [^]D_`aTbdcIedef3`%gih=>(DVuG D t u# wuMywyzy

L A uD HyzywyDa t A

$# *$

+b‹hV_qžObik`oLpkb`byLj%bFxjmh@b o@[%]@g=bFxLl@[%b"xLbFn%g=[~i¡vbFx¨ikyŸj%hLi€n(oV_4oVb[Fu._ayVxSjmbFnwj%bFx·ikj]Oy_+yLl@`vVb[]4©

b={V_4`oLpkbFn > /Ii¡yVxIpk}o@[%]4žIixLbFx¨vL}SŠ‹_4[gj9êb E l@[A¦„œjnxIi"7 g=lLpkj j%] ©t_qik[wpk}g=]O`oV_4[%b,j%h@bYEŠ `bj%h@]@x

™ikj%hj%h@b`bj%h@]@xxLbFn%g=[wikvbFxh@b[%bOu@vbFg_4lVnwb]4©j%h@bxIi"@êb[mbyVg=bFn ikyik`oLpkb`byLj_4jwik]Oy*¦V§Êh@bIEŠ!`bj%h@]@x

o@[%]O^I[_4``bFx2vL}Š£_a[g 9/bE@l@[ 4â‰86@i€nvV_InwbFx]Oy>uO_4yikyLj%b[%o@[%bj%bFx©ªl@yVg=jwik]OyV_ pVp€_4y@^OlV_4^IbOuO™.h@b[%b_On

j%h@b`bjmh@]x2xLbFn%g=[wikvVbFx2h@b[%b\i no@[%]O^I[_4``bFx¢iky 7¦F§bFnwjwiky@^7hV_In*nwh@]4™.y_4v]Ol@j*jw™]]I[xLb[n/]4©@`|_4^IyLi¡jmlVxLb

xIi"@*b[%byVg=biky [ml@y jwik`bOu@h@]4™bžOb[FuLj%hLi€nÊi€ny@] xL]Il@v@j7xLl@bj%]j%h@b$ik`oLpkb`by>j=_4jwik]Oy£xIi"@*b[%byVg=bFn¦

O]I`bb={V_4`oLpkbFn¢hV_FžIbvVbby,©Y]Ol@yVx,j%]|g_4lVn~bo@[%]OvLpkb`|n¢iky‹j%h@b2oV]4pk}Lh@bFxL[_qpprikv@[_4[%}O¦/§™]|xIi"@*b[%by>j

o@[%]OvLpkb`|n;hV_qžOb‹vbby byVg=]Il@y>j%b[mbFx/¦.§h@b B [nwj(in,_4ySyLl@`b[wi€g‹]4žOb[V] ™ o@[%]OvLpkb` ¦.§h@b‹oV]ap¡}Lh@bFxL[_qp

prikv@[_4[%}+ob[w©Y]O[%`|nb={V_Og=j[=_4jwik]OyV_qpg=]O`(o@l@j_4jwik]Oy*u_4yVx‹yLl@`vb[n_a[%bnwj%]O[%bFx lVnœiky@^ ,Iˆ;vLi¡j$iky>j%b^Ib[yLldG

`b[_aj%]O[n_4yVx;xLby@]O`ikyV_4jm]O[n¦I„Y©jw™][_4jwik]OyV_ pMyLl@`vb[n_4[%b.`lLpkjwikoLprikbFx/uM_4yVx(j%h@b[%bÊi n y@]g_4yVg=b=p€_4jwik]Oy*u

j%h@byj%h@b+nwj%]I[_4^Ob[%bIlLik[%b`byLj©Y]O[;j%h@b‹[%bFnwlLpkj;i€n;j%h@b+nwl@` ]a©j%h@b+nwj%]I[_4^Ob;©Y]O[;j%h@b‹jƒ™]+]IoVb[_4yVx@n

>Ç`bF_Inwl@[%bFx i¡y·yLl@`vb[]4©7vLikjn=A¦§h@bnw]4pkl@jwik]Oy¥j%],j%hLi€no@[m]OvLpkb` i€nb=ikj%h@b[(j%] lVnwb_Yn#!"l:&(%k8T

'&=#nJ8lk3 'k' iky‹™.hLi€g%h‹nwj%]O[_a^Ob7^I[%]4™7n j%]`bbj7xLb`;_4yVx/u@]O[.jm]iky>j%b^Ib[wiTHbj%h@b2žOb[%jwi€g=bFnvL} _Ox#G

xIiky@^ _Ix@xIi¡j~i¡]IyV_qp\g=]IyVnwj%[_qikyLjn ™.hLi€g%h #gmh@]Oo]D@ %2y@]Oy;ikyLj%b^O[_ pžOb[%jwi€g=bFn¢™ikj%h@]Ol@j.b={VgmpklVxIiky@^ _4y>};]4©j%h@b

iky>jmb^O[_qpo]4iky>j=n ikyVnœi€xLbjmh@boV]4pk}Lh@bFxL[%]Oy*¦

§Êh@bnwbFg=]OyVx9o@[%]OvLpkb` i€n_.`b`(]O[%}]4žOb[V]4™·o@[%]OvLpkb` ¦1n.ikžOby_ xIik`byVnœik]OyV_qp/oV]4pk}Lh@bFxL[%]Oy™ikj%hZq

g=]OyVnwjm[_qiky>j=nuF_On/`;_4y>}_Inq

"

žOb[%j~ig=bFng=]OlLp€x2vVb[%bIlLik[%bFxikyj%h@bxLlV_ p[%bo@[mbFnwby>j=_4jwik]Oy*¦F§hLi€nb=@*bFg=jwikžOb=pk}

prik`ikjn.g=]O`o@l@j=_4jwik]Oyj%]nw`|_qprp*xIi¡`(byVnœik]OyV_qpo]4pk}>h@bFxL[_ ¦§ÊhLin o@[%]IvLp¡b` i€n_4^O^O[=_Fž4_4j%bFxvL}j%h@b©Ç_Og=jùjmhV_4j

j%h@bg=l@[%[%byLj¢i¡`(oLp¡b`(by>j_ajwik]Oy"_qprpk]g_aj%bFn_ B {@bFx‹_4`]Ol@yLj]4©ù™]O[1/ nwoV_Og=bj%];oVb[~©ª]O[m` _;g=]O`o@l@j_ajwik]Oy*¦

eWxL}>yV_4`9ig$™]O[1/nwoV_Og=b™]OlLp€xvbvVbj%j%b[¢ikyprik^OhLj7]4©j%hLi€n.o@[%]IvLp¡b`,¦

O.y,j%h@bnwl@y@yLikb[nœi€xLbOuj%hLi€n.`bjmh@]x±hV_On.nwbžOb[=_qp¸_OxLž4_4y>j=_4^ObFn¦dEik[nwj.]a©\_qprpÇuj%hLi€n.`bjmh@]x±o@[%]xLlVg=bFn

™b=prpê`9i¡yLik`iTHbFx±[%bFnwlLpkjn\iky _g=]Iy>žObyLikbyLj ©ª]O[m` ¦>§h@b¢ik`oLpkb`byLj_4jwik]Oy;i€n žOb[%}|n~j%[_qik^OhLj©Y]O[%™._4[x/u4lVnƒi¡y@^

çYÿæ/ç€ý

o@[%]@g=bFxLl@[%bFn9©ª[m]O`Aj%h@bo]4pk}>h@bFxL[_ p7prikv@[_4[%}O¦ 4ikyVg=b‹y@]"[%bFxLl@yVx@_ay>jv]Ol@yVx@n_4[%b^Iby@b[_4j%bFx/uù_In2ikySj%h@b

E ]Ol@[wikb[(CŠ,]Oj1H/Iiky`bj%h@]@x/u@™bb={obFg=j7jmhLin¢`bj%h@]@x;j%]vb`]I[%bb=7 gmikby>jq¦

E@l@j%l@[%b b={ob[wik`byLj_4jwik]Oy2i€n*y@bbFxLbFx2j%]b`oLik[wi€g_qprpk}g=]O`oV_4[%b j%hLi€n*`(bj%h@]x2j%]¢j%h@bù]Ojmh@b[*jw™] />y@]4™.y

`bjmh@]x@n¦

•/µ@´ °¶ ·°@’F‘

+bjmhV_4yd/ Š‹_4[=g 9/bJE l@[©ª]I[hLi€ng=]4prp€_4vV]O[=_4jwik]Oy£_ayVxj%h@bb={V_4`oLpkbFn¢h@b^>_qžOblVn¦

† F'*¢

4c6 7¦/eyVg=]Ol@[%j_ayVxYE¦/„Ç[wik^O]ai¡y*¦ >g_4y@yLiky@^£o]4pk}>h@bFxL[=_ ™Êi¡jmh MOWpk]>]IoVn¦;„Çy&O$ :Dn Dn

&=k:!"' i$ &('klk=J '&('!!"! &(% &('nnJl D OuOoV_4^IbFn ,OŒ8C R Z@uOe Š O„ nZ 9/e2u

e ŠZ[%bFn%n u*cFŒOŒ@cI¦

4ˆD6VvLik^OyLikb™ùhV_a`|n(/Iit¦'D 'i$5ki 8i&('l Q #i$D¦§bFgmh@yLig_ pʅbo]O[%j„œydG

j%b[%yV_qpZ\l@vLpói€g_4j~i¡]Iy"ŽIŽ>cOuL„ƒ…„ Oeu/…by@y@bFnuE@[=_4yVg=bOujO7g=jcFŒOŒ,@¦

4<,D6@¦GE¦ ù]4prp€_4[x/u@Z¦ E bF_4l@j%[wikb[Fu@_4yVx;§¦L… i€n%nwbjF¦ dl&%#kl W V!"= &(nPln^ 3'!5

k% dl&O' ¦§*bFgmh@yLi€g_qp\…ÊboV]O[%jŒ,8CMcR u > g=]4pkb.]I[%`|_qpkb Ol@ozb[wikbl@[%bxLbI9ê}O]Oy*uVŠ‹_q} cFŒOŒ ,@¦

46Z¦uE bF_4l@j%[wikb[F¦ _4j=_ V]4™ _4yV_qpk}@nœi€n]a©$_4[m[_q} _ayVx¥n%g_qp€_4[[%b=©Yb[%byVg=bFn¦#"%il8&%'l i'!%$ #&=i'!

'&('!!"! &(=&('nn #Ou@ˆZ#>c A Câˆ,8CdR,@uE@bv+cqŒOŒ@cO¦

4<RD6Z¦YE@bF_4l@j%[~i¡b[q¦ Z_4[_4`bjm[wi€gWikyLj%b^Ob[ o@[%]O^O[_a``iky@^V¦ &('")&* & =k8&(k+ J&('li8!!"Fu

ˆOˆ#>O, A Câˆ4,CˆD;O‰@u Obo+cFŒO‰I‰@¦

4<;D6IE¦L„Ç[wik^O]4iky*¦ 8$ 8i&('l &IX0 &:!"'Jn8$?'$ &I!"=Yil&(k+' F¦ù§bFgmh@yLig_ p

…boV]I[%j >, >Š‹ZWG ùe7„ GljO‰DG+>¢cZOˆ e7„+F„u5> g=]4pkb-_4jwik]OyV_qpkb Ol@oVb[~i¡bl@[mb|xLbFn7Š±iky@bFnxLbZ_4[wi€nu O7g=j

cFŒO‰O‰ ¦

4¡Ž6$¦.@¦d2lVg0/M¦/ :l&=#kl#&O n :#l&0I'$0 n :#l'ld¦1@¦¨irp¡b}_4yVx O]OyVnu243ucFŒLŽ ‰@¦

4‰D6Š·¦9/b3E l@[Fu5@¦G 9\¦Z_ HF_4jFuO_4yVxQE¦4eyVxL[@zbO¦ l'lk3n'6' i'!"8 & n !"7 nnl'lR

=j ¦¸§bFgmh@yLig_ p\…bo]O[%j2ŽRLŽ>uL„w…„ Oeu Obo@jmb`vb[cqŒOŒ,@¦

4ŒD6§¦ V¦Š,]Oj1H/Ii¡y*u¦…._qi"@_@un¦ 9¦§h@]O`(oVnw]Oy*uù_4yVx…¦Š·¦ù§h@[_ pópǦ §h@b£xL]Ol@vLpkb+xLbFn%g=[wiko@jwik]Oy

`bj%h@]@x/¦=$ &( 8F:9<; :!"=kl=$ ' &0u*cFŒR, ¦

4kc8ZD6$¦¨irpxLbO¦=' ul)&('&= & !"8%$ &O' !> 8&O' l ¦ §*bFgmh@yLi€g_qp…boV]I[%j7„œy>jmb[%yV_qp¸Z\l@vLpói€g_DG

jwik]Oy‹Ž ‰R u>„w…„ Oeu/…by@y@bFnuE@[_4yVg=bOu bFgcFŒOŒ ,@¦

4kcIc6Š·¦>.¦++]4pr©\_ayVxŠ"¦d9*_a` ¦ 9/]L]Ooj%[_ayVnœ©ª]I[%`|_4jwik]Oy(j%h@b]O[%}|_ayVx_4y _qpk^O]O[wikj%h@` j%]`|_q{Li¡`9ioHb2oV_4[_qpTG

pkb=pói€nw`,¦="?,1i&O' d'kld ' &O' !!"!'$J l&=*)+l=$:8ln^uˆ >ǍdA C͍#ROˆ8C>@ŽOcOu)O7g=j2cFŒOŒ@cO¦

æ*æ áutqþ=þö=ö

Unit´e de recherche INRIA Lorraine, Technop ˆole de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS L `ES NANCY

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rh ˆone-Alpes, 46 avenue F´elix Viallet, 38031 GRENOBLE Cedex 1

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