Memory-based scheduling for a parallel multifrontal solver
24
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Memory-based scheduling for a parallel multifrontal solver Abdou Guermouche (ENS Lyon) — Jean-Yves L’Excellent (INRIA). N° 5162 April 2004. ISSN 0249-6399. ISRN INRIA/RR--5162--FR+ENG. THÈME 1. apport de recherche.
(3)
(4)
(5) !"$#%&' ! ! () +*, !#-,..*, !/0 1243,57698:6;=<?>(576@%A;CBEDF GIH0J75LKNMPORQL;TSLK UWVXL;TYHZ[D]\ @T;=^_^_;=Ka`bBdc!F efcg1:M hjilk-monqp
(6) ~rt!Ts
(7) +n-u%|.v!nxs
(8) wTn%y7z{wn-~ |.v!}Lvg|!k-mon%v s
(9) wT a g|.an!n%!iln-! iln 7pxr
(10) ag4Trt: wTn%v vwTm²¦%n¬xwT=|³wT ag!¡n%n?7¢ ®¯ylv!-xhjwTa©ilnfn a|gmoil!nqn-§amomo©n-mon-gmo}£vP°]ylghj}´v¤wTiayl©v.nCv¤wT TwT¥nq ,v!n-T
(11) ¥
(12) wTaw!n%v! v!n(-wTg7 wT§,!n%n%©n-v
(13) -j|77}±v!!n%wT¦-m:n-|!©vbv!xv!¦!wTiln-¨xn%°(7§,yan(µ]|gailm³bnC§avg|g§l n%wT|g¶|!|gn-©n-|!l©(n%n%v.v!!| ª«|gwTi|g|!wT©| moiwxL¦7n¿¸·w³xwTL|g©±qlv¹ ,T¥|!n-|g±il|gnjwT| ,w|!vgª7vm:an- a !n-xl¦n¿an-|glil-n
(14) }mon- wTmo aiNgº±}on?ylzL v wTn-gn¿moTn-¥4»wf|!v¼ vgwTil wTx½£©n-|g,im³wTya|¼vg|gyl¸¥À!!io»|!| n%wT Niav a©¾»¦yln-n%xv º Á¿C~¼Â,° ÃÅÄÆÇ!ÈÉ =Ê¢ ± wT!v!n¬mqwT|gg©%n%vPºam³ya|g¸¥À!»| wTmon-|gil±Ëºv!!iln%7yaalºmon-mog}. ÕÙëWÕÙÎÐÏ×æÌÒÍTìxÎÐÏRí?í¤Ñdî ÒEÓPïÀÑRð-ð!ÎÐÏ4ñ-ñ-Ô¤ñÕÐÏ×ò_Ö.ó!ôTÔ!õxؤö Ô¤÷¤ÎÐÕÙø%Ô¤ù!Ú=ô ÕÐÒ]òåú-Ô û%Ï0ð ü=Ô]ý!ÛdþÒ+ÿÏ×ÒgÔ!ÛdÜEÍÛdÒWÝÖ¤Û×Ñ4Ö¤ÞaÑdÍTҹ߱ԤÚÖ¤Û¯Ô!ÑdÖ?ÎàÛdÒ¼á=ÒÕâ ãåä=Þ[Ö¤ÛdæÔ ÑdÎÙç%èTÒáPè¬éaÔ Û¯Ô Õàê. Unité de recherche INRIA Rhône-Alpes 655, avenue de l’Europe, 38334 Montbonnot Saint Ismier (France) Téléphone : +33 4 76 61 52 00 — Télécopie +33 4 76 61 52 52.
(15) . 4
(16) * & ! . g, '.³ g/ ' ! ) g* !#-
(17) * ¢ L%-ya wT|g©mou-mo!njan%vRmou-|gil±an%v07!n%-|!n%v4 ,n-ya|-|g!n¼-g|g©¾±yln yaRw!u?®
(18) v v!|g yawT|!|gu-©©n% vwT wT!©ak-©n]aan¼wTlv!}L%vgn-|!mok-mon-»n%|vR7}±luxwTwTm:!n%©¾±v0yl-nf!n-w%y7}»zwTa±|n wTyalan]§7| +wTn%-©|gn¸¥°aµ]nn¹! u%wT7 aya !ng|R a ±!%- ya v!wTn]|ga©n% v mo u-wTmo ailn!n(anoanÅau-% n%n-v:lamon-u-l|g%ilnLaan%n%vxv³° | !£iln%©vxn%ºvol%ylmvf§amowT±»|g|!w%l¦v n%Å©n:a ,n%vo|!n-mo±±|g©7n-¸]·¾±xwTy |g ©»l| v%vgn%| v³wT|gvg©|g¾» ylwT|!n%u-vq©7n%y v v!ya !aw amou-wT|glil%±n-amon³n-m³±|fya |g¸¥À!ya»wT| mowT©nu-º,©C!n-Á¿C ~]L%Â,-° ya wT|g©mou-mo!n ya v!¦n-ya wT wT©k-©n §wv!u É x Ç ¡ ¢ mqwT|gg©%n%v¿-!n-ylv!n%vxº7mou-|gilLan¬m³ya|g¸¥À!»| wT©nº,!aawTl%n-mon-»|xº,mou-mo!n.
(19)
(20) "!#$&%'(#)*+,- ./ ! 0.1#2 3 5. 4. 6
(21) *¬ R* !. !¥×|±n% 0 wTia|g!ailv ©n]n-¾»70yln%!!vn-n%-|!wT¿|0|gmov!¦n-n-¦|g}ilnLwTwTaggvnjwTn]lmovg n-wTmo!v! n¼gwT} vgg}7|g!vg©n%-|!¾»n-yayamowT!v4n-Tmom¥ln-ya±l|g|!¸nxv¥_wT!%0±n%m:| ¾±wT yawTwTmo!|gn%©n-:|glil|!vx±¿°9a8¿|!vn-xwT ½]!wTn]n-|g¦!¦n-njx§aºmoyl|gvgiln-||gn-ilwT}³LlwTa!vn¼nv!7qª±¿l-|gP©in-½»wT || wv Tx:wT7wT§a®¯%!|¯n
(22) }° n?z7n%-ya|g©q©vl|¼wT½]wx}Lv¹ ,v vg§a©n°;:¯|©v|gi±ylv¹-gyl-wTl|!³ a|gm:=<xn|gilnmon-mog} > nqvg|gyl7©n%´@?pxBA¹|gilnmon-mog}´§n-iw%¦L©ya³T¥j|giln: wT wT©n-¹mya|g¸¥_!±| wT]v ¦n-&CEDC-F-G wmoT?H47ln-º7(mo AN|gil|ggin}CwT7±|©%v!yl-|gv yagn% §avwTya§,|g|g©©|g´iÅTv!T¥| ¥wT|g|g|gilil©fnn³wTv!| lwvg¦ªLn-7v
(23)
(24) }±¥À»wT
(25) |!m: ©|gwTfil wTv nf!©il an-n%!0L7n?%yazan%n%v!a-v!ya{!|gvxwT©I° al a> v!nfxwwTi Cilw%¦n%§vn n¥×v!n%m:n- aC|g!il|gxni¦mqwTn%Ë|.wT°¬|gilhjwTni»n-wylmo-v¿|gn-½]¦»nn| a|gil!n mov!n-n¹mog|g} ia©v§n- iwTw% ¦Ln-©Rlya(n-½¶T¥mo|gn-ilmon gv!}»®d§¦n-wxv!°)n%hj7}LilnwT·lm:!©v!¼|(v !illn%n´7ya%lavg©vgmo|!v(n%!i wTaw¶©vgmomon-v0mo|!
(26) g}»m:®d§ aw!xv!n%¦ n v!lw%nb¦nq%v ln-©%n%n--g|gl©v: |gilvg|gnb wT7|!}Ln-wT}m:¥×©fv!|g!ililnon%7 yawT wTa ©n-¼T¥.| w|gvgilªLnbv| 7wyavggª7va(wv |gvgilnol¥×n%w¶-|!|! g=<PwCwT|g a©!LN%°bn%v!hjv!ilxnq° v hjn%%iln%lv n momon%n-mo iwTga} ©vg§mowTvjwTwTlm%nqwT§,|n-!|En%½¼7n%yln--¶a|g³iln:|gil an!mo±%n-n%mov v!g!}ovx°o±%hj-iaya© v³wT½¼|g©g{ª T©¥,v|gilwn
(27) ·lv!!vg|¦n-vg¼|!n-wT l:|!x½jm:wT a!a!Pv ¦±wamo|gil!nn ¿©v¿§wTya|gv!ln%ya(|g©wT´|!n-|giwT(||g½ia©v¿| wTwTª n n-x§º|g|gilin ½]an%gvgª±© wT ¥¹wTmol!nmomon-mon-mog} g}»%®Ewxl½]vgwT|g !wTn:»vg| |!vfwT|g©» |!v!Å!ilwn%%7%yaya»a|x ° v!hj|gia wT©v|!n- wT©n% ,vn-©v.©vwT©v!g»¦wTan-g= <x}{n%m:w v]¥Àg| wT©»P½|x° vxJ° :EÅÂLn%-|g©7º7½¼n¬!n%xwTNv!monn-ln- wTRmon%!iwTa©vgmov Tv!|g¥NwT |gwTwTil|!n
(28) n-©n-m³}©v!°yam .|g¸¥À¥À|!M!n-»CE|g| DiwTC-wTËF-|xmoGlº°2n-|g:¯il ÂLLn%ÂLË-n%K°|g-©:E|gb©bIÂL7n%°lp-|gººN©½¼½¼Ln.noa4f an%!½]v!n%-n.v!gn-»§,|¦n.nw{v!wflmoan-n½n%v!-m:mog an- a!mo|gx©¦n-gmo}»T®dn-§¥N±w|g|!v!ilv]n%n
(29) I|gimqvgwTwT|w%¦½¼wTnonn-v mqmon-©wn%n-a-»|gn.|©|!T ¥ |gmoiln-n¬mov!w%g¦}±n³®Ew%v ½jn-©wTn%!-n |g©| w(vgª vg|g mqwT|!wTn-wT}{n-mo¦n-n-»Å|Åv!|gÂL wTn%|!-n-|g©} Å¥ÀlK°> |gilnfn( a| !wn%v!v!ªLn-v{»|vg| CwT|gÂL©xn%wT-|g}«© wv!7v!°Ðolwn%7}L|!IwTm:|gil©n aT¥!L%yan%v!v!ln-!vP½ N° :Evg|g ÂLwT|!n%n--|g©©n%ov7IºT½¼|gn¼ilno a!mon%v!n-n-mo»|v!g}´mo§n]n-in?zLw%¦L ©n-gyamon-T»¥| |gwTil7n!n%v!vgya¦|!n-v4 wTyllvg |g wTvgil|gxa½ |gililxn¼½ m:v!| wTw|g-©| wT wTmon-|!n-!v
(30) xwTŧnmo±7¸·n%|!om: a!x¦nf|giwT|.m: w-|x°JOwT}ºa½¼nf%l-ylan°. ) +*, !#-,..*, C* ¬ ¥×:E´g#m:|g./il Un:aVC m?º0wbya|gvg|giyl¸wT¥_%!|o%n%±wTv | !vgwTnb©jw wTv! av!TL a¥]-! wTwwT|!g n%|giR¶wT?H|!SaCº+¥×wTBnx-A¯w|!ºR i¶|ggil=<PlnwTL|g¥×a©wn{-l|!vTg¥¿T=<Pw(¥jwTvg|gv mq©T®¯wT¶xwTT©a¥n%n-9|glilv wnn:v mqv!mqn-m³wTwT|g|g§agg¸©z } %n%©|gv³vf!n%xanwTl©W/n%On:L§»!ya} ! n 0n-.1pY+X® ! n-wT ag!|!n%Yv v Z:n-»|gil|g$n ab![|gil.1#nÅan-§a ©±n- lª,aºn-lwT©-v }(C§xn-wT|¯½]©n%n%\ n- !| w] ^vgªL vP-°.,hj_il n³ ¥_!§a©±L| !wTªºmq½wTia|g©g ¸i9zC%©v
(31) g7!n%¦Lv!© ,an%lav »|!|!C|¯|g½¼iln P. Q. `9` #ä acbed(fg.
(32) . c =
(33) EV = .. ¦mqwTwTg|gwTg¸§az©n%NvwTl|giCwT|g|qilnwT!Vn¥× 0w./-|! U
(34) g=./<x Un%£ ½
(35) =ilen-= ºN|g½ilian{©!n-i´m:%g!wTn%|gvg© ¨lawTv
(36) |!{g|g|giailmn¦ awT!g±wT%§an%©v n%v!v¿n%v |gi|gwTil|fn{wT¥_!!n±ya| 7wT® |glilwTn|!n%%½»|gilgn-§a:ya a|g©!L %n%§av!vg©La!ª´|g©ilv³n] ¥Àw!v!v!»n%| wTa|!mqCwT|g|gilgno¸zË ° wT
(37) !n-l±%|njl|gilLnjan L° wTg>¨|gwTil7n-¥× w-%|!g±= |g<PgwT§a|g©ya|go©©lvv %¥_m:! am²©n-|!wTnº ¦ iawT©yl7n%!v]n-I%wT»!| nowTlw%¦n%wT{wT§a|g©n:iln.¥À!|g»il| nwT, wTmq!wTn-±|gg|x¸ºËz|gTil¥Nn-}C|gilxn.wT wT§!n-n:± |wX?v!°v!n-hjm³il§an¿©n%n- m:W_d°ànwT°³|gvg©yam:wTmon% g½|gia|gm i ©|gvjilwn |gilnfvg|!wv !v!an-n-m³¿§a|g }bw%¦|gn-!!n%v nwT° W_½]nal|¿ a!L%n%v!v!¿ wT!n-»|¬lLan%v
(38) §n?¥×!n³|giln-¬!ia©7!n- X ?px A0T¥ 5 6 1. 2. 3. 4. X X. 5. 6. 5,6. X X X X. X. X X X X. X. X X X X. X X. 1 2 5. X X. X X X X X F X F X. 3 4 6 1,2. 3,4. Oya!nop#Z&mqwT|gg¸z(wTlb|giln³wv!v!L-wT|!n%(wv!v n-m³§a}{|g!n%n°. X X X X X F X F X. d¥mqhjwil-wT|!n|ggwT¸!z vxºL?ÐBglA¯|g°n.ia|!m ¿ yavgylg| v!wn%a v¼ ªo|gia|g|gilil!n%nnCn%|gwT!!»n%nxn(|gwgvj|g§a Tyawx¥R¦|g©n-vg|!!v wT §awTdº©Ln¿|g!ilª7bnCvxºLw³mowT%ln-mob±wT|ggl} yl|gvgil yln-wv%mon(ln-!n
(39) mon%¥À¾»yag¼}q!|gn%ilvg¨ n
(40) w-§»%ya}ngº7!|gn-ill±n(n.|j¥d¥À¥_w!-¼±|!|g| il!wTnv waTn-½j w%n-}7lvq7a!fP½:v{|g½ilian©nÅ n-|g ilwTn(|g©v!| lwv!mqª wmoan-#n moZ½gil} n-:WÀ%|gil»nj| wT wTag|gawT9a|g¥×wil-nC|!%g= »<PwT|gg|g©§aya|gT©¥ w
(41) ¥À§a!©±» | ªLwTv aXmq¦wTwT|ggg©n%¸z v ©vj a a !Lvg%|gn%©v!v!Nn%ºË½ºlwiln-%±|gil|ggn¼§a¥À!ya|g»©| (wTa§amq©LwT!|gª{g¸z©v©v4vg| ¥×w gªmon%bn%:½wTial©!i(wv lv!n--m³!nx§aw©v n%n%Ëvº»|g|gililn¬n]vg%=<x±n¬|gTg¥4§a|gyail|gn¬©v!o| w§a!©ªLa!ª7 v moT?px¥¼Bn-|gA¯moil° n g } ian-©¦7!n-ya´|g©l±´a©n%vv¬¦wTn-!gn }C!an-n-mo xn-¦ln%a´n-»¥_!|m ´|g|gililnnvgw| v wv!!n-ª m³wT§al}C|g!|!n%vn vg=|!<xn ,a©n%-!}nxºwv!wn%v¿vP°¬§lhjv iln-gn ¦v!n%| ´w!ª ! ! " l*,* " ² ! CDECF-Gbylv n%v³w%m³§awT|g©9T¥vg| wT|g©qwTlI7}LwTm:©ov! iln%7yaaCvg|g wT|!n-©n%vP°qhjia©vf©v³an?® |!|Ev }±-g nxn%§,wvn%!iT¥0l{ LwTaa n-nfwT| wT©©vn-©vj©wvgv!mvgM wx?Hl4B¦ANn%wTwTlwT\§al©n³n³? |EA¯}±°L hjCEn³ilDTC-n¿¥F-%Gc ZwTm: awTya©n-| wT©|gvg©mÅ°"©Ovj7yag!¦n n-bq§»vgya}om:|gilmqnwTwg=v!<xv!n%n-vm|g§ail}qn³7|g!"!Ën%nn-!wTn-l» | ã$# `Rã&%.
(42) .
(43) "!#$&%'(#)*+,- ./ ! 0.1#2 3. P0. P0 P1. P0. P2 P3. P2. P0 P1. P0. Type 3. Type 1 P0 Type 2. Type 2 P0 P1 P2. P0. Oya!n¹Z. Type 2. P0. P2 P3 P0. P2. P1. P3 P0 P1 P2. P3. P2. P3. P3. 0zawTm: a©n¼T¥l7©vg|gg§aya|g©T¥lwjm³ya|g¸¥À!»| wTlwv!v n-m³§a}|g!n%nx¦n-R¥ÀyaR a!±%n%v!v !vx° hjnxwil!n
(44) i·l§a! vgwT|¼l|E!}±ib Tn
(45) ¥yl|gv!iln%nvj|g!an%n.}ox|gwTilon¿§»n|g|gg!nxlwTvg|!©n%o wT wT ©wTn- wT©vgm©n-d°l¨7yl|¯%}Ln% ,{n§»}ln|gilln¿±awn.v v!©n-vm³vg§a| wT}|g©x|gwT!n%n#} Z !w iav!vg©|g7il!lnn-n%! n%lvg|!L|IaTn%¥vRl|giniawx© a¦v !n¹± §%wTn%n% ,n-v n-v! X%:wT½m:!n{iam©wC!yai«av!©n- ax| wT!±|!Tn%%¥.Ën%|¯v!° }Lv n% ,v:nxnCw%¦|opqnj½lvgLyaila§an-n%|gv:!n%%wTn%v ±jWÀ|gwvggv m:§avgya a|gl©}³n%I«xwT|!§a©(©n%L |g!ilª7 nbcv:
(46) v ¥À./wT! moVm n a|!T!®d± a%!n%±v %v!n%v xv!°Rhj4ilmqwTv! an¼ awT!ana©n-v4|!yln-gv!m:n%fl|!n%
(47) f§ylwTvgwTal¿%n¼w]|g|!iln¼ 7®¯%axm:½ a:yawT| wT|g©g|gwTiaam ½]?pxgBª³ALTwT¥ll|gfiln¹wvgv!yaya§a§a|g|g!!n%n%n%n?v® »|!:|gilnf a!±%n%v!v !vx° h¥_j!il±n|!v!v¹n%%l|gil:n
(48) |E}±w v!v nn-m³%§ag!}n%vg|g !n%n
(49) lawTv!n.|!f|g!wonxwTp |! n%q wT wT wT©n- wT©vg©mn-,TwT¥Ël|gilwTn]!¥_n
(50) !7±©| vg|gwTg§amqyawT|!|gn%g©%§»n%vx}:° §a ©LwTg!ª7nv T%n%¥]v!!vgPa½ovx°{vg|!n- Nº wTN. |giln¬ a!|g±il%n-n%!v!v v W f ©vf3 ! ilX.wTv n-!n¬!vgil| wT|gv!©n-xwT7}´}±7wTyam:g©axÅwT|g}biln§wvgv!}±n%mŧ,©o½] ag!ª±n-© a!wT ® §|g©wTlwTvÅl%Tn¥%|gillnv!©¥_ayan- }wT|g©vgyalm:vx°Cmohjn% iln a¦|Å. §a©L a!ª!L° %n%hjv!v!iln mq©vfw!vgn%|!v!n- ,Ål a!vgL§a%©n%nqv!v!¥×ų|g7il}LnqwTn-m:m:©xwTw=} ® | !ilwvgLª7vxv!°Ån%vhj|!ilvn{v!%w%¦gn!n% avg ,!L%ln%7v!v!a´!v.vgwwx%¦%nq!| 7wv!aªLv |!wT!nq|gil|gn-iln- ½¼wg-ªL|g©¦wTw|!Cn% wTlwÅv wv!v!Lvg¶lvwv|gil|gn-ilm n-}IlwTn-!½ n !n% ,%n-n- wT¦|gn%©qlvvg|g|gilnvg|!´w%¦§n
(51) nÅvg©aanl°0nhjº]il½nil½¼n-!gnŪL©aw}9mo|giln-nÅ|gg© ©n-v wT|gil|g©nl»vqyam³%§gn-!jn%vgT ¥ l7wT|gaIa|!®d |gil»n| n-wTgm:n-wT|g|gi©wTÅ9|g ail!nf±%n% v!n-v wTwT|g!©nol| wTvª¥×n-¶.w»v!v!|!n- mw§a%%'} X?ya° »| W_|gilv!nbwT!nwT¶!an- T¥mqwTa|gylan. `9` #ä acbed(fg. . SUBTREES.
(52) . c =
(53) EV = .. lhj-}L±il-anÅn©³º |gia½7©!iavg |g©!gi|¯§a}Lya© ,v
(54) |gnC© a!Tű¥%© v.n%v wTwTv! an%wT( a©n-©§±n%©}CÅv!mÅwT¥ÀºR½ a|g!iliaLn©%!i¨n%¥dwv!v!-©|!v!v¿wg=<Pyl wTvg|ga© NwTÂL° xwTw ©n-¿©vg~ mÅ.ºµ%l?Ð%n-A Zglw{v{ |g ilnŧa!©LL!ª | h|gjililnn{vg=!<xiln¬©T%¥4n|gilTn¿¥|g¥_!iln±| |¯wT}LË mqn{wTT|g¥g© %wTn% vxwT°J©Oln-©v!m²|gilnan-|! n-lTa¥4v|giln9|g|g!iln%nqn¿|g ilnvgmq|g©wT¶ a a ao|gilTn{¥|¯|g}L!n% ,nn:ºp¿wTll¶Lan% v %wTwTl!nÅgb!n%§amqv! ,wv!n-l|! n-7X?!ºva(wTTl¥4¥×£|Ew}±- |!nf!vxwT°{lgÁ¿±navgn%y±vwTya©m³v}ºN§v!| n-|EwT}±!|gvb ©fnTwT¥¿bl al!LLa%an%n%v!v}bv!wTwT!!vxnomoºiav.wTwT§|jiIya§|wT SwT|glil²-nqawTv ¥¬v!|gn-|gilm³ilnn§amo}´n-mo|gwT!|gn%gna}{Wå®d¥ÀT !¥|g»il»|!n|v a7 !¥×Ln-% gn%wTmov!|gv!©vl|gv¬iilwTwn-!v
(55) !nvwaTv¥0l|!|gviln nfa%|g|¯g}LwT!R ,n%vg½]n qglª±l7©±aawn%oÅvx±°|gilya¹nfm³w%§ in-vg
(56) | aT!T¥ L¥%wTn%v!NwTv!|g|!¿avivg®dyaw §av|gwo!»n%| n%±vx° 0n- TwT¥|g!©nxlw7vxJ°}Å:E| awvg|gª7wTvwT}lºw µ|g]g©n%lv{%n-|!g9a!ailIL|gv!iln nÅvgaw%¦} n|gv iln-n©n% a-|g!©L% n%v!vgv!|g !wTv{|!n-©n%}v!v+®d¥À©wa|¯}Ln%¨ nÅ|giwTl±a|!n%v!vxn-¸º¼¥gºnxw½!i|gi W_mqv!wmov!|!nCn- X awT!»±ya%n%wTv gv!|E} |g|g%ililln¬nv!mqv!|g w%wwT¦v!n%»|!vn-|!xvx©°°Jv:Ew{vjw§awT7wTl|g©%n%N(ºL|gwilvn¿ ,v!n-v!©v!n%-§a|g©©n
(57) {½©|gv¼ia|gillnn¿½]vgyl!gi{ª±©|giwwT(|]T|g¥4iln¿|gilwTn¬mo%yag!±n%|jvg T¥Nl½]7gaªoo| w¦vgn-ª{b|! Master (P0). Master (P0). Slave 1 (P2). Slave 2(P1). Slave 1 (P2) Slave 2(P1) Slave 3 (P3). Unsymmetric. Symmetric. Oya!n$4Zh¹}± nflLan%v§a©± ª±aq½|giÅ|giln¬an?¥×wTya|
(58) vg|g wT|!n-}°. jh g!iln-n(ya§a©wT±¹ ª±¥Àa¹¶|gilylnv!vgn%}L£m:¥Àmoon-|g|ggil©.n(x|¯w}Lv! ,n$nWÀv ´n%n lO4Lan%yavq!n"©vq4[!X?n-ºqyawT!qa¥×n-¼o|!¬|gil§nCwTyawTllvg%}Lnm:|gilmonn-½¼|gg©(gª:x§wn-v!n|¯½¼wTn%ln- v>!w%n ¦nfvgilvgPya½¼§an%| wv!ªL vx° ?pe4BA0|giwT|¿|giln w-|g¦n mon-mog}ŧn-iw%¦L©ya¬T¥KCEDECF-Gq©v¿l|
(59) ¦n-g}(±L¥× wTwT m:wT©
(60) ©n-v!]!n?ilz7n%n%7-yaya|ga©lvgvP|g° wThj|!i±n-yl©vfn%v¼½¼|!nqf am:!n% av!n-!P»¦|n.|gil|gn.ilmon:n-lmon?z7|³g}ov!n%§,-n-|gi©wxl¦±v©v!ya]moTn:¥Ë|gmoiln.n-mov!g¦}±n-®Exw%;° ½]> wT!nnb·l7!}±vg|® ã$# `Rã&%.
(61)
(62) "!#$&%'(#)*+,- ./ ! 0.1#2 3. amo!n-n%±v n-|!v»| |!:w{|gmoilnn-movg|g gwT}±|!®dn-§w}v!° n%O4 vgwTw%¦}nºlv!½¼n-nf©n%-|g¦©nIwvgl|g n-wT½&|!n-7}L}°wThjm:il©n-¬I| w½¼vgªnqav! n%ilv!n%-7gya§,nqav!qmo|gin:wT|¿m:wT amo!xv¿¦wTn?|® m: a!P¦±a|gilnmon-mog}b§,n-iwx¦±©ya¿T9¥ CDEC-FGa° , . !¹/ !R* ! a*j* " :E |gia©vfv!n%-|g© ½]n:an%v!-g§now{ln-½ mon-mog}»®d§wv n% v!!iln%7yaawT a a!w!iI|giwT| wTmov³wT| !wTn%7ylg-|gaiaCm |gil|gnoiwTvg|{= <xilnon-T l¥v{|gilw no av!!| ±w%!ªn%v!v moqn-mo|!Ig}´ il7±yav gnÅa(|!v{|gil%noT®dn?½¼zan%g-ªyan-|g!©vbN° :¯vg|¬wx©¦v n%wv{¥_½ya|g}´i 7mo}Ln-mowTm:g©} %nxwl i´v!|g awT!±»%|!n%vxv °v!hj¿iav ©v|gwTiwT|g|g|gilianm xwT!n%¾±aya! an%!vfL%7n%¥×v!v!gmq wTW_|gmq©w vg|!wTn-§,¬Tya¥¼||E}±|gil non:moon-lmoLaYng}X
(63) xLwT% -ya! ilwTL|g©v!n ¶T|!v¥ v!w%¦n%v.w%%!7a|!:|giln-mon-mog}b©wË°J:E|©v¦n-ŧn-©x½ Z ÉÄ å n-mog}»®d§wv n%Åvgw%¦n³v!n-©n%-|g©(vg|g wT|!n-}° ! a n T 0 ¥ g | l i ¬ n a y g ! n » | À ¥ ! » | T w 4 q m T w g | g ¸ z ÂLg||gilnj ,|!n-±|gwT vgwx¦nj a!±%n%v!v !v:!x½a³!an-¼T¥ |giln-mon-mog}±%-ya wT|g© ·llI|gilnq§an%vg| º4±yam³§n-:T¥ a!±%n%v!v !vxºv!Å|giwT| ©v vgÉmq wT©n-|gi|!wT Å|gilÊ nfÉ vgya+¥dw%n¬T¥0|giln¥_!±| wTNmqwT|gg¸z Ä 4Ê ¦n É !x½v
(64) T¥|gilnfmqwT|gg¸zb|! a!L%n%v!v! »wÄv!yavgm³ R§ n-|gilnT¥ !n-mqvgw%wT¦an%v aq !P½v.n%¾±ya| wT§a}b|!:nxw!i( a!L%n%v!v! °° 4Ê h|!jil!nilwTLv!ng|g|gilianm vgmq ilwT±©n%v v!n%|
(65) v:v!n-vg|¿w%¦Tnb¥ a a!!±L%%n%n%v!v!v v!!!v.vo|gwi%wT%|¿!7©a§´wT|!}Å §|gwTiln-wTl%mon%v¿n-mo|giln³g}¶mon-©mowËg° }(:E½||g|!iln-layav| v!lw%-¦!n%nxv¬wv!|¬a·l!|gv!il|fnv!-yag|!gv¬!n-|g»il|¿no ,nx|gwTilªn-º !v¬wv¿Ivgilx!½x½a^CO!ayan-!n³Tl¥]° |g>«iln-ilfn- mow:n-mo a!Lg}%n%©v!v!wË°oiwhjv
(66) il|!n-q il|±7©v v+n ® |g|ggiln
(67) §ayamo|!n-n%mov¼|gilgn}!wTPl½v¼ aT!¥Ën%|gv!iln-gn¦¥_n%!v]±|gil| wTn
(68) -mqyagwT!|gn-g±¸zq|j ,nxwT|gª ilnW_¸ a¥R! L%v!n%vgv!v!§a©nY!vX?°0bhjilwn ½]p wx
(69) }o®d|g§ai©wT±|¹ ª±§a|giq a§!wTL7wTyll%%n%n% v §±v!i}wT|g ,iln{nfwwTv³ gO4|giam)ya!¥ÀLn 4(§n?z7|g%in- a|gil| n¬|givg}LwTm:|mo|giln-nq|gg»©fyamwTl§,bn-:yaTl¥vg}±!m:x½mov n-|g9g©³nxwx!wi¶v!n% vjwT½g|gN|g©iw%9¦n½|gil¼n³§v n:wTmo¥dwTn mo!nfg!n-yawTx° . . .
(70). . nf ront . i X. i. (M EM [i] − M EM [j]). j=1. .
(71). j=1 i (M EM [i] − M EM [j])/nf ront .
(72). . j. .
(73). `9` #ä acbed(fg. . 1 i. .
(74) S. c =
(75) EV = .. Current memory peak P0 P0 slave selection. P1. P2. P3. Oya!n¬cZn-mog}±®d§wv!n%(vgwx¦nfv!n-©n%-|g©(v!|g wT|!n-}°. ×¥©
(76) vmo©x½g!|gnfaia³%m m:wTp(g a|!©©vn?v{z½¼an½n%vg½|giÅlmon%%«l!¥×%n¬n-q»g|g!§ n-wT|g|!yai«n
(77) wT|goil§an|g©ilLvgn!}Lª7m:yavxl°movg}Ln-m:|gg©mo n-wT|ggl©«xyawlv!vgn}Lvgm:lmo%nn-|g|ggil©n vgx}±wm:v!n%movx° n-|gg:¯©«.|gillnn ¿L%-|!yan wT|gi|g©wT|bo|gTil¥,nC|gmoiln-n%¹ i awT!a±©%vgn%m v!v yl!v!v0n%©¨v0|g|!il¶n]§a!§7gwn%a-|xwTvg¥|bw
(78) ¥×7¥Àg|ggilmq%wTm:|g©a ¬!|!n-n%!wTia|ga¦©nxwT|! ¶!n-|g ,ilng|xmo°;:En-mo|giag©} v mohji±n%yl ivxwTº4a|gil©vgnomź|gnxilwn-!!iIv³x awT!L%wn%%v!v!-ya¬m§aya!wTw|!nqax|gwilv!no|!vfl|g-il!n:n-mo¦wTn-g»|!wTvx|gº©|gIiwTT|¥jx|!wTv¬Imo§,n-nmo gvg} |g½¦ilnon- fl|³n-L»%wT-|gya¦!nvxº° mq| v wTn-»wªv!|fn|!n-§±|gfil}´n- am|g!il±n:%±n% a|!v !Åv!±%w!n%%v³v %v!wT!yaxn»°_|ªL:El x½w|gail7n-wf|gvf©v!¾±Nyaw%º¦©!n:wbªLv!mo} n-©n%n%w!-v¬i|gwT© aN©v!v!°ovgm §a±©yln-n!li¶§»vgya} wq!n%|gmoilv³n:n%|g iiwT|gwT|filan-|g©!ilvgvm nqv! b©ilv|gli©%n%wTn%%|fvn%|gv!ailv¤wTn-gl} }(nox¥×§»wT} nxw iÅ a!L%n%v!v!|!:iwx¦n³w:%iln-!n-»|wTl(wvya 7®d|!T®¯lwT|!n³¦±©n-½ wv v!vg§a©n¬T¥0|gilnfvg}7vg|!n-mÅ° ¿gv0} an%7v!¥×-ggmq§n%wT|g©wT§xn?¦zan!º±i.wTan%go|g§±ia}m)|gilpjn il a±!±v!%n%n%v0v v!|gil!njvx°vghjwx¦ian%©v¹v0§xwTwqv!n%x:wTylv!n.|gv!iln]molnvg-| gwT»|g| ©xwTwTln%vgyl|gyv¹wTmo|g©n-mlv® wwx½]vwTvg!iln:P½T¥¹9|gil n Oln?z7ya|
(79) !| nwv!ª ZoWÀ v½Xil|gn-i£wT|w(½ a!0±%§,n%nv v!|g!:nxwT!|!iln%L´v!n%Cv:|gwTillnvg|gilwxn-¦on&° l:¯nbw|givwTvg|¿wx·l¦nyaº!n|ºm³|gilyln vg|ln-§½ n | wTwlv!Cª³|g|gia!nx©vwT|!xn%wT:C§±©}nxw|giln|!bvgwxwT¦Cnj al!-±!%nxn%wv v v!nT¥¹xwT|gil:n§, n]nx¦wTn-ªÅg}T¥¹%movg|gn-mo} :g}|!°fn-g±moylv!i´T¥ vgmo|gyn-wTmo|g©gl}v±i%w%-ya¦n wT§|gn%©n- | v wTn%§l-ªLv |gn-©ag¿¦Nn%° »|!f:w a%!%n-yam:»|wT7g¥×} gn?mqz7 ,wT|gn-©gomowTn-±§,|!v ya|0W_l!nx|w7!n-}f | wgv!|!ªLn%vx:°4ilhjn-ia!Yn ©v0X4©|gvi|gwTil|n¼vgil§7x½]gn%n%-:|T|gil¥n]|gillnn%%¥×n%v!©vgx½|E} aT ¥ ã$# `Rã&%.
(80)
(81) "!#$&%'(#)*+,- ./ ! 0.1#2 3 Master. T. Slave. Processing of a new task Problem with the coherence of memory informations. Time. Time Memory information. Oya!nÅZ. 0 l z T w : m a © n l y g v g | T w g | a I g | l i b n l % n % % n ! v g v ¯ | 9 } T ¥ a ! % n 7 © g | a | g l i Å n w g | ¦ T w g | © « T
(82) ¥ ! x n w 7 } | wv!ªLvx° 6 ' /
(83) * *, * ¬
(84) !
(85) l*j* 4 " ! :E |gia©v¬v!n%-|g©´½¼n a!n%v n-»|fv!monm: a!P¦n-mon-»|!v|!b|giln 7}LwTm:©mon-mog}±®d§wv!n% vgwx¦n v wT!m:iln%7aya wTa|Åvg|gg n%wT-|!|gn-a} av!| !wTn%|gv!©n-»|!7n% ¥×g mq|gwTil|g©n 9 a!n-9¦L©|gilyln{vf7v!n%}L-|gwT©m:N©° b> v!!n iln% a7!yan%v!n-a±´|¬|!|¯C½]bmqmowTªn%nb!i| wTamo©vgmo!nv n 7q-©n-±|x_° :EIwv!n%%l´ wTg|xºR½¼n: a!n%v n-»| w{mon-mog}±®Ew%½jwT!nq| wv!ªv!n-©n%-|g©¶v!!iln-mono|giwT| %l%n-glv.|giln¬lLan%v.wv!vgln%vg| wT|g©xwT}b|!qw a!L%n%v!v!x° . Slave designation. .
(86)
(87) ! "# $ % & '( '( #)*,+.-/ "01 324 5+6 !
(88) ! 7 )8 9/*. ¿ ±iv¿|!wT vgwilw-x%|!½%n-g´ya=<x±n%|:|g|g§»ilil} n nq|g a| ilw!n¼n-vg¦±ª7¥×w©vf-yl|0|giv|gwTiv!| wTn%|0-½|g|g©il¹n-N}³§ºnoi|gilwx an¦!njL7§,%}Ln%n%v!n-wTv!:n%m:Rvg©| wTW_|gmo ©xn-wT|gmoilno}:glw}±v!nx®Evgw%wT½jlwT¥_ya!n%no |gyavg|!!|g¬nY X?wTw
(89) °(|!n-±¦yl©n-n% :vi m a| !ylw±v!vg%ªL|n%v v | v!wTwTª!xnn ° h|g4il(n%v n-nblvg| yaw!vgn{ªLvw§n?L¥×±! nbmo|giln-n-mo} gwT}´!nb§,|gn-!inxwxwT¦±|!©n%Ëya° xº0> ½]nno7m³©vgyl|gv!|³a aya!©xvg¦Li£©a|gniln|gil| nowv!ªL7v¥×|ggimqwTwT|q|g©wT! n!n-lv!wT©|ganb¦n|gil|!n lv!yaL§aa|gn%! v n%X?n%° v,W_|E}± n{pflLan%v X.wTlC|giln| wvgªLv¿T¥|gilnya a ,n-¿w%}n-!v¬T¥|giln|g!n%n W_|E}± n{pºÐq&4 `9` #ä acbed(fg.
(90) px. c =
(91) EV = .. 4Rx Ä»Ä hmojiln-mon vggya}±§a®d|g§!wn%v!n%n%vx7wT}± wT§m:n©¦]n-vgg|g}« wT-|!gn-|g}©xm³wT¬ylvg |4§,|!n¼n-gw%mo½]vwT!Tnj¥T¥amo|gn-ilmon0¥dwg-}¨|R±|gi%-wTya|0 wjwT a|g!©± %n%v ?pxv!NA¯°©vNhj|g!i»nxylwT|gvxºaw wwavg9ya§a|!|g !n%|gnil|!nb ,w%nx¦wTª9©ÅTw¥¿mo|giln-nmov!yag§a}|g!Ln%%n-º¹yal wT|o|g©!nxw lil-n%!£nxw}v!n-n | W_X?|g° iln¿¿mo|!n-nbmo|gigwT}|oT|g¥iaw ©v:vg½]wx¦n¿ya©| £wvg§ªonb½¼moya©vg | §ln-l|!n%n?9·- wT?¸px¥¹%A¯°¶m³hj§aillnbn%mo n%|! biwowTavg©| vgwTm|g© ½]vgnÅ aa|gn%|gvga T©v¥¹vg§yaw§av!|gn%! n%n%v¿ ½mo|gin%v!v¤wowTwTn%gveZn³moln-%monÅwg} a!%±%vgn%|xv ºv!wv v!hj| iawT©gv.|!vq!ilw´©vg%yan §aWÀ|gv !n-n%ln7ºja|oo§a|g!ilnwamoxn-wmov!|!vog}b|gil ,nÅnx%wTªbvg\| T¥W_|gmoiln-n¬mov!yag§a} |g! ,n%Yn nxX]wTcª ©vXmoT¥|g|gil¦n(wT|!n%%l§»%}{n-g|gliln%n ¥dwv!ya-|§a|g|g!in%wTn| ° |g§iln-n©aw-|ga¦ nÅ|!mo n-vgmoya§a|gg!}£n%n%xvowT«wT!in{w%!¦n-nCwT|g!¦nxn-wT|q} ¦vgwTmqgwTwT|gj©¶lvq|!n-lgmovg©av:nT¥.w´ avg!ya±§a%|gn%!v n%vgn awTl|g£mo|gni°´wT|hj|gi»ilylnvo| nxwwvg ª7i v a7!¥×L%gn%mqv!v!wT|g¬©iÅw½vw{N¦±§©nn-½ ylv!Tn%¥]|g|!il:nov %n-©n%vg-|f|T|g¥¼il|gn¬ilvgnqw%vg¦yan%§av|g¥À!n%n%v¬|E}±§ n-n³a l|gL!nxawTn%|!vxn%° ´|gilno|giln-!vx°q±yl i. Ä . a = É Ä x Ä±Ä |gTµ]i¥¼wTwol| %ln-½±gaajna°.v!{±hj|gil¶ilnfn¬vgmo| yawT ag |g|:n-¦wÅwT |gmq©wTwgC|
(92) vg|!©Tn-v
(93) ¥0 |g|g| iilwwTnfvg|
(94) ª@|g½]!W_n%n|gniºlv!wTil½¼|nfyaxwTm©C ylw%vg§¦|.no§©Cn³wTgwT§anY¦L©X?n¬°\a|!{:ElvgwTawx»n%¦|gn%n³©Ë-½]º0 ¸wT¥.g|!ª½¼nn{|!|g{il%nwolw avg-!©|ga±¦n-%wT n%|gv |g©v!il n lv!WÀv L|gn%yan wTnO|gº ©wTC ya!Tn¬l¥ -'!OW×nxw[wXv!yan :!nqT|gil¥n|gil½lnfilwvgn-moil!nn-n%mo a!±gl}%n
(95) n% v !v!n-nx awT³ª!n%v ½n-½»4|!vjL%|g|gil-!yanxn
(96) wT
(97) |f¸©¥ § awT!|g,Lil%monn%n-v!lv!monxwT g}¥_ya ,|g©nxyav¿wT!v!ªnon-©w{n%§l-v!|!wTn-n%ggC¦nn%wbv¿|E}±vgvg lwxn¦%npn |gmoiln-n³mo§,n-g}±®da§awv!an%b Tvg¥w%|g¦ilnn¬v!¥dwn-©-n%|!-|gg©= <P wT|gvg©|g wTX?|!°.n-hj} ilnan%v!v n--©n%g-§,|g©n%IT ¥ |gilnow av
(98) !n-vg¦Lw%©¦ylnv³½v!n%4-|gL©%-Nya°b.h4½C|giCw%¦|gil© n v!ayl!li nwqÅ-wg|gvg©xm:wT a©vgn|g½jywTw%}{|g©ylNvgºNa½¼:n |gilm³n¬ylwvg|v!v! an-m!n%§a7©}-||g!|gn%ilnn:° w¿-|g|!¦n¿wT|g|g©iwT´|.Tw ¥¼| v!wylvg!ªqi §| n%w%vgª7movx°n%vjhj!ianx©wv¿7x}bwTl§%nn wTwÅ4mo|!n%vv!v !wTianq©7|!!Ån- |gilinqw%¦nln§,n%n- C ai!wT±g%n%nv v!Tn%¥Ë|g°.ilhjnqi± ylwTvx!º,n-¸»¥¹|n-l¦n-Lga}nº4 a|g!il±%nqn% av!v !±.%n%|gv !v!nxwT³|ga¶Å!woiwT iag©nbTv ¥n-l|gilanv :E|wTx!n-wT±o||gªLilln-qx½v vn-l|g:iwT|g|.iln|gia%©vvg| |¹wTvg¥ªq|g½ilnR%§,gn%!%n%vgmo n¬l!7nxwa7³}{| wCv!ª w |!f!n-wTwT|g|g¦iln-n} a!vg±mq%wTn%v Rv!wT!movx;°ya:¯q±|
(99) waT¥07|g|g©moNnº° ¸| ¥wv!moª,º!n³C|g|giilwTn Cv!n-|
(100) lnfT¥| w!v!nxª{w7§}(n%%l±moan%n%vxv
(101) º !|gnxiwwT7|¿}ºli|gwilv.nf|gil an!L%wTn%gv!v!n%vg¿|¿%moln-mo%n-ggl}Ån%C!n%v ¾»n-yala!n-vmo|giln-n³±|!%vx° v!|.OT¥wT|gil}n º |!a
(102) ln%v %|g-nilgn¼w
(103) §,| wTn%wgvgªn%ilvgn-©|4v!n| ww-©v!|gvª¬¦|gwTi¦|!wTn%n-Ë| ºxwT|g il njO§, anj!yaw±-!%no|gn%v!¦' v wTW_|!§ 0n%X?%Ë° °l>
(104) %n-n:glxn?zlwTn%qwTm:v!v!n-n% aln©nja|gv0Ti¥l|gwTil|g|¬iln]|gn¹liln-nm:½£ 7%w¥×-vg|g|0mqT|g¥lwTi|g|gwTil©|n¼ %mowTgn%!§!n%ivgya ,wT|¬a©l|gvgilam nv v!l|g%ywTm:|g©aN °¼mqhjwilvgn³|!n-7¥À| wgvgmqª7wTv |g©©v lilv
(105) n- 7¦¥_yan-j(|!§± }{w%|g¦ilnf©£ a!wTn-¶¦±©lyl-v
(106) !nxmowv!n%nb!iTwT¥.a|g©vgilmon{v
(107) mo|!n-:mo7¥×g}Igm nx|gwTilª nf9|gil|gn-ia!©vv . . P0. P0. ã$# `Rã&%.
(108) pp.
(109) "!#$&%'(#)*+,- ./ ! 0.1#2 3. Memory. Memory. Memory Memory peak. Memory peak. Memory peak. Without predictions. Slave selection for P1 P0. P2. Initial memory. Activation of a master task P0. Memory sent by P1. P2. P0. P2. Ô ÎàÑdÍ=Ö?è=ÑNÝPÛdÒgá=ÎÐÜWÑdÎÐÖ¤ä. Memory cost of Master task. . Memory. Memory. Memory Memory peak. Memory peak. Memory peak. With predictions. Slave selection for P1 P0. P2. Activation of a master task P0. P2. P0. P2. Ú ÎàÑdÍ¿Ý=ÛdÒ+á=ÎÐÜWÑdÎÐÖ?ä Oya!n³Z]µ¼g|g©xwTRvg|gywT|g©Å½|giCw lLanfT¥0|giln¬ya a n- wTg|.T¥|gilnf|g!n%n° Initial memory. Memory sent by P1. Memory cost of Master task. . `9` #ä acbed(fg. Estimation of the memory of incoming master task.
(110) xp c =
(111) EV = . n½xwTw§iav!© ya}Åi|:½]|gilwnÅ
(112) v|gvgilyan¿§ag|g|g!lian%vgn%m| vwT±wTp| l° wT9l:¯ln%|gailyln%nvn%Ëlmoº±n-¸a¥mon%½]vqn gT}¥
(113) !ºan-§±|g ail}nw|g%ilyann a|g vgilyan-n³:m mow%Tn-}¥|gn-g|g!©ilvnylTv!¥¿ln%vg|g(| ilwTnb¥×»|
(114) |gwT!l|gn%ilnÅn%nxylvgwTv. wxmo¦§n n-nbmov n-©n%gg}-n%|gº7-©|!|giln%N n º yawT±mo a|g !±n-ya7j±yl|¿w%%}Tn%n-{¥!mov§±}:n-| wmo|gv!ilª,n.gºL}l|giln-l½«n¬n%n%wTmoan%n%(!gi§»|gwT}iaam)©|gvgilmo½nfvx-°Ëya:¯gv!!n-n-©|gn%±il-|¿n.|vg!|gyan%il§avgn|]|g!vgTn%¥Nw%n ¦|gwTn%illvnÅwT l|gwTbil n³n-!¼n%mov!½] ,n-n.mon%-½|gwT}Å yl%|gv!iln.vg|.n
(115) T%¥l|gilvgg|gnf|g iawTlmn?»z7|!pv| |!:an-l|!n.g|giam p½iln-!n¬½¼n¬ylv n¬|gilnmon-|gg©³an%v!-g§n%ÅwT§x¦n° . '( '( #)*,+ 3 ) 1/
(116) ! 4 1) 9#*. :E£|gia©vv!n%-|g©. ½ ] Å n a ! % n ! v n ± b | w o m n o m g ± } E ® % w j ½ T w ! n | w g v ª ! v n © % n g | © ¨ ! v g | T w ! | n } R> n(§,n- §»} ° | !an-wn%m:v!v ª£-gl|go§ailn|gai(|¯wT}L|¹|g ,ilvgn¶now%¦§p nn-i| w%w¦Lvg|EªL©}±v¼ yawTn´!nT ¥ wmq-C|gDEw¦C-vg|!wTFn-|!Gbn%{| Iwwvgv|!ª7n-v!vbgLmovgqv| wTTw|g©¥vx|g| wTilwvgn-}¨ª7}vfwwTv v!!vg nil!n%ln%7%n%yan-¨¦a|!n%Il:°L|g§»il8
(117) }nn-|g!il an:n!L½] %ilnon%v!mov!v!n-nxq!wTv vg wx½]§»¦} nn a!L%n%v!v!x°hjiln-(½¼n¬ a!n%v!n-±|
(118) yaln-½ | wv!ªmqwTwTn-mon-±|¿v! iln-mon° . L. L. ... L. L. L : Leaf node (Type 1) T1 : Type 1 node inside a sequential subtree T2 : Type 2 node (Master task). . . . T1 T2. zawTm: a©nfT¥w ±NT¥0| wvgª7vx° CDECF-G¶iwv(w %'eT¥!nxw7}¨| wvgªLvPº.½iln-!n nxw i | wvgª¨%g!n%vg ,lavÅ|!£w¶l±an´T¥ |giln mqw|:v wTv!%n-m³wT±§a| n%wT}lvq|g½!n%|gnai¨° }¶w´:E||gv!il©| vnbw!!m:ª9nx ,wmo7}gn%| !wTi| ±wwT|fvgaª7©|!vvg{mÅvgl| ° wT|g|!:E©nxwT|g|giil}wTn(|¬wa|gv!iln?vgn¥dwTl ,yan%L|q90vg|!|g© vwT|g©|!±iln-xnbwT} aºj!|!|gLbil%nÅnxn%wv!| v! wi vgxª9°¶ a!|ghj±i%ilwTn%|onbv v!½ ,Lf.wTjl§© nv v§ n-n%©%n%-mo|!n%n% v¿©!v nxw|gil7nb} W×wTlnb0|! v!|giailn{©7|!!n- ´Ti¥.wx¦|gnilnb§,n%vg| n-w ª, a°!L:E%9n%v!v!wn%a0 7X|g©|¿N©v¿º¹ a½ylilvgn-il£n% w(l L|gailn{nT|!¥. |gilTn{¥¼|g|g!iln%nn ½v!wT| ia|gwil©! ªi:ya°hji{n-ial|g©n-v]ia ©wTv!v]m:©}v al©m:n.|mo|!wTvn%½] |giilwxwTnj}LavwT©movgwTm) a ayan-±©lx|¹vgwTyaT§a!¥ ©n%n¿|!vjn-m:qw |g-ilan
(119) n-wT a g|g}³wTi7 ®×mowT·l!n-©n-vgmo|,¿xgw|g} v nwxl¦K° n%n-:¯n%!aav wTn%|gËwTT§»¥R}} |gº±il|g|gilniln¼n.w¥×v! wv!-Ln-|!m³ §agT=<P¥Ë}qwT| |g|gw©!vgn%ª7Nnv ºº |g%nxiw± wTiC|j| wT|gvgillyanv¬§a|g©wT!nxn%wxRn³¦|gn%ilylvnfvgTa©¥0nxw=w ¥wvglya¦L§awTa|gg!n%wTn%v¿»n¬T|wT¥!T|gnf¥0il|gwTnfil|gn!n%wTn³w v!| %gwT|g|g±ia©|gxm wTyl§»}C} ylwv.v!?pxvgv!Bn-A |&X?l°jn%W×wT( l|!b!on-m: a|gil!n%anfv!n-m: a±!=| L<xwTn%|gn%©|gv!ilv!´n¿xTmoº,¥0v!n-|gmoilgnf|!n%g ,C}{Lv!T ¥ ©Tv]¥|gil¦nn- a!LL%On%v!v!ya¿!n ©v
(120) L°ya
(121) lwT|!|!n¿n% |giwwTv¿|jv ¥×±¼ |gilwnv½]wo| gwª±vg©ªÅw§Ln%®d§%wmov!n%n%v¿7!}Lnxw7wTm:} ©W_¬d°ànv! °.il©n%v¿7yalv!an-gl|!ºan%|gCiln¿©|gwil n ya Ll) wTX0|!½n%iln-½!ilnxwn-v]Å¥×|gil¼nf|gil| wn
(122) vgmoªqn-©v.mow-g|g}»¦®d§wTw|!n%v n%{W+7° d}L°àn½wTm:iln-©(v!!|.il%n%7lyavgyaamon%|gvilmon
(123) n-momon-mogc}gX?}q° 7¥×gmqwT|g©b©v Subtree 1. Oya!n -Z. Subtree 2. . . . ã$# `Rã&%.
(124) pe4.
(125) "!#$&%'(#)*+,- ./ ! 0.1#2 3 L. L. ... L. Subtree 1. L. . . . T1. Pool of ready tasks of P0. T2. Subtree 2 Task A Activation of new tasks. Memory occupation. Memory occupation Memory peak. Memory peak. Cost of A. Cost of the current subtree (Subtree 2). Activation of A (Type 2 node). Oya!n$SZ. Activation of the nodes of Subtree 2. zawTm: a©nfT¥w:-g|g©xwTRv!|gywT|g©¥À|gilnf| wvgª{v n-©n%-|g©N° Current memory occupation. . jhaLiln%nv al!|§a©| n-wTmªn½|gil|gni mo|giln-n³mo§wg}Cvg© ln%vg|gn% awTn%|! n-§±}(}(a|gn%ilv n-g| w§,vgn%ªCC»C|!Å|gilwn%% a!yan-¦L±©|¬yl¥Àv
(126) |gwTil nwTv! n-wT©n% a-i´|g©©v
(127) |gTi¥]wT||giln| l½Lilan-no!n{|giwwT a| !½L%n%¹v!v!§nfw©v-|g|g¦!nxwTwT|!|gn%Ëa° ´:Ewlavgyan%n%§a |g!¸n%¥n½]wTnl %ilwv!v©awÅn-³wT|ggiln{novg|E}±|gy wTn|g©b lLa¦non-¶|giwT |O§,n%%ya!mon n%Sv !©vnxwwT7!}nxºw|g7il}Cnf-§gw|gvg©©x³wTvgI |g WÀvgwT|!|gn-ywT}b|g©½´4n?z7|g|g ilwn³-|.©n?|g¥À |ilX?n¬°hjwTgi»yln³vl|g±ilan n%n-¦vgn-|ÅT¥¸¥|g|giail©v
(128) nflmoLn-amon½g}±w%a-yaC yawT |g©|! |gLil%nb-ya% wTvg|g|©TN¥.° |g
(129) ilnbvg|gyail§an³|g!n%|gnÅiln-wT¿li¶wT|gliaË©º,v¸¥xwT|g9ilnf©nx aw! L%|!n%´v!v!wC¿7a wTn-mqw%}7wTv
(130) |g©x|gilwTnwl--|g!nx¦wwTv!|gnb©T¥.T|g¥il|gn{iln³mo|¯n-}Lmo ,ng} l LnxwTaª:n:½ya±|g,¹l|g|¼ilnolvg-!|gnxywwTv!|gn©;° >¨§,|gn%i{%|gmoiln.n%v³ aya©n%gv! vf-v!gn¿|gT©¥4xwTw% ¦WÀvg©7|gyawTo|g©vgyl ibwvg|gil|gynowTg|g©i»N | ºLX?½¼º|gn¿ilan:n%vgmon-lmon%g}w mo½0!n§v!n:w a-ia|g©vg¦|gwT©x|!n%wT|!n%(| wT| ªLwavgªv!mon-©n-n%mo-|g©g}C %wTlvgg|g |gwTiam±|!vfWÀ.±|!Ågw|g%ia%m ya»[|xX?° ° O4:¯|
(131) !!v!il|xLº¸¥jv!n%wv a|gil!±n³%| n%wv v!vgªb|giiwwT|v v!v!| yawT§ag|g|!!n%n%n.w{|vgwya-§a|g|g¦!wTn%n|!n%wTv]l|jvg¸}7¥¹vg|g|!iln-mqn³| wTw|gv!©xªÅwT©±}x°wThj|!n%ia ©v]©v¹§|giln%n xwT|!ylv! n¿Tvgya¥¹§a|gil|g!nn%n% vj±xwT©v¿§§,nn-¦©n-ga}qn?az7b |!n-lvg|gil¦nn wTg|!|0n-gTmo¥|gvilTn¼¥|g!mon%&nn-moWÀyag|!}(vg©ylav n]wTw
(132) nvg"° ya§a:¯¥0|g!|gn%ilYn n X?ºl|gLilanjnwTwT|¿|ggil|gn³iam |! ´v!n-©Tn%¥-|!|gilvn| ,La}³R§¸¥n-©|aaLv¿n%v|!lq|g|4ilnl-ya! anx wv n-n |g|gilg©nqn%v¼mo|! n-mov!n-©gn%} -|j wTnxlwTª |giln-§l]v!n-| gw¦vgn%ª: §±}ov!l%¦±nqa|gilnq ag§,©n-g|¯a}a|!a³ |gilTn.¥l|gil±noan%¥dv]w-§|!n-©g=a<PwT|ga©N|!°
(133) |gil|giln.n-vggya½§a©|gv !nn%ºn%vP| º |gg}La{|!o!n%vg n%-|
(134) |gilnan- a|gi7®×·l!vg||g w%¦n-!v wTwv
(135) m³yl i´wv
(136) v!vg§a©n$° W a{|!L:¥dwT.¥À!m . `9` #ä acbed(fg.
(137) -p c =
(138) EV = . |g|gil!n%n¿nawn-- a|g|g¦i7nf®×·lvg!vgm³|+®¯yav!nx| wTwT!l n%iÅyl|g v!w%}¦n-wT!lv¤wTÅN%l-ya!©nxqwv!|!n¬n-l|g{iln¬|! ©l§-wT!nxNwmov!n¿n-mo|giln.g}b±yaylm³v wT§n-n° X T¥R§a wTl!iln%vT¥4|giln ÉÄ å n-mog}»®Ewx½]wT!n³| wvgª{v n-©n%-|g©CwTg|giamÅ° | gÄiln¬ Rl ±an¬|gilTn¬¥0l|gilLn¬anf|!T Å¥0|gTil¥0n|gil|!n¬ ( T±¥0Ë|gil©vn¬ ,lLv!©a n³ wvgya§a|g!n%n Ä Ä _ ÄÉ N|giln¬ ±NT¥0!nxw7}{| wvgªLv WÀvg| wTg|ga:¥À!m |giln¬|! (T¥0|giln ,L) X Ê É g}{ moÄ n- nxmo RwT ªg} §l v %n-gvg¦Y| n%W_() Xvg l%-nyag|g!iln-n¬±|§n-mon-amoaag} qW_T¥0l|g-ilyln7¥dwa-o|! gnx=<PwTwTª|g©T¥ v!ya §a|gÄ !n%Yn X mon-m® Ä _ Ä Ë§,n-©av.|!ow:vgya§a|g!n%n Ä ÄÄ 4Ê 4 Ê Ä R Ä Ä4 Ê R É |giln¬lLanfT¥0|giln|! (T¥0|giln¬ ,L 4Ä Ê 4Ê .
(139). . .
(140).
(141). . . . .
(142). ≤.
(143). . .
(144).
(145). .
(146). .
(147). .
(148).
(149).
(150). . .
(151). '0
(152) * +* > n³vgilya©{·l!vg|mon-±|g©(|giwT||gilnfan%v!(T¥|gilnwTg|giamov
(153) T¥¹ÂLn%-|g©lvlº7°pfwTlC7°Ð v!h4wTil!n{x½vgwT|gyla!7nxo}:w|g7|gil} iln-n¿|gilm:n© !§n%wvgwT-ya|j4nT|!¥4Tn%|g¥
(154) -il|!w(n
(155) vx° 7wT}LgwTnm:wT©movg|gya ±wT||!n-T¥.©n%n?vjz7 a !n-g ,mov n-n%»q| wT|g{©|g iln¿wT al! n-¦±½]©noyl¥×vjLv!-n%yl-v³|g©iln-l!vxnºL½] n |g|gn?ililz7nbn
(156) n-~ s.g¿yamos.|giln-¬»n-|:+ ¥À !ya L:® %jvg|gL ©n-n%wT-|!a|gn-©© %n%
(157) v°0©n%hj¶-il|gv!©n.n-¦|!n%n-vg ? YA|!wTv¹¯jºi a|gw%!il¦nbn
(158) §a©%§,n-n%mon-©n%v-|g ,WÀv!©n-n%+n{¥×h4¥_g!mowT§am n%©qn Á
(159) Yp aX|g¦n?ilz7n-n !|gvg :wj|¯-}¶|!n%TI¥ÂL~¶¥ÀO!©vgm²}7gvg©l|!n-n-w m|g qiln-T¥ : s :g¹%m: v!n% T¥ v!n-¦n- wTLl±an%vT¥ 4. a!±%n%v v!!v4nxw iN° ¹w!ilLan¹©vn%¾»ya a n%½|gi w m:amyam T¥T T¥4mon-mog}vgiwT!n%(wTmoaq|!vI4:~4P½¼n-gW+pºH4 8 <BX¼ a!±%n%v!v !vx° "' ìxìxã_ä=í-í-ÏÀí í Ñdî î ÎàÑdïÀïÀè=ð-ð-ÑRð ð ñ?ñ?á=ñ-ñ-è)ññ(0òò©î!ë+ ¤?Ø-û õ¤ÒWóa %ÕÙÖ¤÷-òÝTx÷Ýú% $# ÷7Ò+æò_ò%óÒW&äxP#Ñ,ð ò©ÒWô= Ñ4 ù- ð!á=î Ò+ ?-+Ï ûõ-`R xð%Ò+õ?õgÏ×î!ù-Ï× ¤÷ Ö?û=èPõ¤Ûdó%Ü+ðÒ+ÏNÒ+äãåä=Þ[Ö¤ÛdæÔ ÑdÎÙç%èTÒ+*PÜ+ÎÐÒ+ä%ÑdÎ-,ç%è=Ò. ã$# `Rã&%.
(160) px.
(161) "!#$&%'(#)*+,- ./ ! 0.1#2 3 "#%$'&)(+*-,. GHJI K*6 Y9V J( 9]J^ I ,+43436 I (J_)Z #$' +J JJ_ H NL#(+*V9 H J6.
(162) . /101232!4 .812!0!6 /O.M5303836 .Z.@2!Z30 835!7343636 .Z!412!534 .0!5L.736. 35 6373836!038 /812!4L.M435 .436!Z30363737 /O.43630!0L. 53735373Z!03Z .Z3Z@/Z!Z@/ .3.6!734383Z35. j_ JZ. .532/8@/. 630383838!030. 93: 93: 93: 93: H 9 H 9 H 9. ! *+; !<= ! >1? @A BCDE <=
(163) F N OM@ !P3 @<Q<Q P <R TSE*VU*-W X %M
(164) L ;<[ \
(165) ! 91B % ;O ; *`+aJb BC@<= ! cCF d O M<=BO
(166) *`+aJb BC@<= ! cCF d O M<=BO
(167) e I !C@P ! @Df6! ;F ! !;O
(168) hg# >1 #P1O id
Documents relatifs