A New Guaranteed Heuristic for the Software Pipelining Problem
36
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A new guaranteed heuristic for the software pipelining problem Pierre-Yves Calland , Alain Darte , Yves Robert. N 2759 Décembre 1995. PROGRAMME 1. ISSN 0249-6399. apport de recherche.
(3)
(4) .
(5) "!# $% !& '()
(6) +*, *-. //, *0
(7) !&1,. 2. 3 4658797/5;:=<,>?5A@ B&CEDFDGCAH
(8) IKJ
(9) L0DMCE4FHON,CE79P/5QJR<,>?5A@&ST(U
(10) 587/P V WXZYA[(X \A]^],_a`cbedcXgfihkjml _ifil9n?Xg_iop?\AX \rqsqG_it qs_io;uwv?\8o_iox?_x?Y(y?y_iz _io"u?Xk_iz o_"\Ank{ _ilo|(o l"_"t ],_io x?jmo l9Xgj}v?n_iz o WXZYA~g_il_i\EW #\Ap?p?Y(XZlx?_Xg_ifihk_"Xgfhk_+y(E AA0be_iz fi_"]av?XZ_`"AAbAp?\r[A_io i"; 8AO_p?Xg_io_"yAl0|A_il\AykYAl9hk_"X0hk_"n?Xgjmo l jmf^MY(Xl9hk_o YrMlg\AXg_,pkjp_iqmjykj6yk[p?XgYkvkqs_"] O_¡v_iqmjs_i¢E_Ql/hkjsohk_"n?Xgjmo l jmf£l YOv?_¡Yrcj}yEl _"Xg_io lv_if"\Anko _jmlv?Xgj}yk[Ao\Oyk_i¤j}yko jm[(hEl-l Yl9hk_ o YrMlg\AXg_,pkjp_iqmjykj6yk[p?XgYkvkqs_"]¥vA|_io l/\Avkqmjso/hkjyk[jml o0x?_i_"pqmjy?¦jml9hl9hk_fij}Xgf"nkjmlXg_il j}],j}yk[ p?XgYkvkqs_"] Od qsoY uj}y§l9hk_-o j}yk[Aqm_QXg_io Ykn?Xgfi_fiq}\8ooaf"\ro _AuY(n?X,yk_i¤hk_"n?Xgjmo l jmf¡jmo[kn?\AX \AyEl _i_ix
(11) u jml9h¨\©v?_il l _"X^v?Y(n?ykx¨l9h?\Ey§l9h?\8l,Y8ª¬«'=O®j}y?\8qmqm|Au _¡p?YAj}yElY(nkl,l9h?\8l"u¯jy°jml oo j}]pkqm_io l GY(X ]ukY(n?X#\8qm[AY(Xgjml9h?] h?\8o&\,qmY8 _"XfiY(]pkqm_i{(jmlg|A ± ²(³
(12) ´gµ,¶w8·A¸kY8Glg\AXg_pkjp_iqmjykj6yk[ uAfij}Xgf"nkjmlXg_il j}],j}yk[ u;[(n?\AX\AyAl_i_ixhk_"n?Xgjmo l jmfAu8qmjsol¹o fihk_ix nkq»º j}yk[ uRfi|(fiqmjmf,o fihk_ix nkqsj}yk[ ¼M½,¿g¾ ÀgÁ" ¿¾ à ÄÀ=Å6Æ"Ç ÈkÉ
(13) Ê;ËÍÌ ÎGÉgÏ
(14) Ð
(15) ÑgÒÓ9Ô^ÉgÕGÏÖ"× Ê"ËÍÌÎMÉgÏØgÌ9Ù Ù¯Ö"×ÚÛ¹ÜÝ Þ ß ÛÝÈkà9Ì×Þ&áâ۹ܹáâãäåæ¬ÉçËGËÍÉÍè6é¹ê/ÉgÕ¹Úëìíì¬ë ×8îÉgÕGÏ ï;×ðë×ðØAÉñ ÊðëË
(16) ì¬ëÜ Égñ òæ¬Ì ×Üó?Ì ô ×8ÉçèFã
(17) ìíÊAÉgÕgä õ Èkë öAÌËÍë9ÏGÌæíËÍÉÈ÷áâå?ø9ùÜ
(18) ã¡ÚÛܹÝ#úgû9ü/ý"øißRØ=Ìì¬ÉÛ¹ÌËÍÙ ë ì¬É¹ÝÖ"Ê
(19) ÉÍñ ËGæ¬ÉçÖ;ËÍÉî"É
(20) Èkà9Ì×(ø;þ è÷ÿ/ü9û/ÿÈ"éÛ ÚÉgî;É ø
(21) "!$#%&'()#*+, &" ( "-. / ,(01)234 5# 6.$#7"8 . Unité de recherche INRIA Rhône-Alpes 46 avenue Félix Viallet, 38031 GRENOBLE Cedex 1 (France) Téléphone : (33) 76 57 47 77 – Télécopie : (33) 76 57 47 54.
(22) !&. . ¥
(23) Rw0¥& cw *! . *
(24) ! 1,. 2 ¤^ *, *. / .!& . ²÷
(25) ²O Yknkop?Xk_iz o _"yEl Y(yko n?yk_ykY(nk¢A_iqmqm_ahk_"n?Xgjmo l j?nk_apY(n?Xqs_p?XZY(vkqM_"t ],_ x npkj}p?_iqmj}yk_ qmYA[Ajmfijm_iqG#Y(nko],Y(yEl9XgY(yko"u;p?\AXfi_il l _ ykY(nk¢A_iqmqm_\Ap?p?XgYkfhk_Au;qí_i{(jmo l_"ykfi_x¬n?yqmjm_"yO_iz l9XZYAjml
(26) _"yAl/Xg_ qm_ap?XZY(vkqM_"t ],_x npkj}p?_iqmj}yk_qmYA[Ajmfijm_iq_il qm_,p?XgY(vkqM_"t ],_x?_XZ_io |÷ykfih?XgY(ykjmo9\rl jmY(y-x?_iofij}Xgf"nkjml o"R_ pkq}nko"u
(27) ykY(nko] Y(yAl/XgY(yko?nk_x \Aykoqm_,f"\8o x?_Xg_io o Y(n?XZfi_io&jmx?_"yEl j÷nk_io"u
(28) ykYEl9Xg_ahk_"n?XZjsol j÷nk__iol [(\EX \AyEl jm_G\;¢A_ifn?yk_v?YkX yk_x?_0[(\AX \AyEl jm_a] _ijsqmqm_"n?Xg_?nk_,fi_iqmqs_,Y(vkl_"y(nk_p?Ykn?Xq¬hk_"n?Xgjmo lj?nk_ x?_ 0\8o9p_"XgY(ykj?_il¸kfihAjm_i[A_iqmo9hkYkh?yª¬«; %_il"u8x \Aykoo/\#MY(X],_ykY(y0Y(pkl j}],jmo?_iz _AuAn?yk_#fiY(]pkqm_i{(jml?_ z ],YEjykx XZ_A ¶R"i´ "!#²) )Wj}p?_iqmj}yk_qmYA[Ajmfijm_iqMuXg_io|÷ykfih?XgY(ykjmo9\8ljsYky¡x?_^fijXZf"nkjslo"u
(29) hk_"n?Xgjmo l j?nk_ioa[k\AX \AyEl jm_io"u Y(XZx?Y(y?y?\Aykfi_"],_"yEl&x?_qmjmo l _AuRY(Xgx?Yky?y?\Aykfi_"],_"yElfi|(fiqmj?nk_A.
(30)
(31)
(32) !" #$ %!& !' " (*)+,)-/.0$$"1)+ (
(33) 2.3/4. 5. 6 7
(34) !^ w ! ¸kY8Glg\AXg_pkj}p?_iqmj}y?j}yk[ 8:9 hk_"Xg_"\;Gl _"X 0jmo\£l _ifih?ykj?nk_Q\rj] _ix \8l,l9hk__;fijm_"yAl^_i{(_if"nkl jmY(y Y8o j}]pkqm_-qmY(Y(pko;=< hk_]^\8j}y p?XgYkvkqs_"] jmol Y£fiY(p?_#jsl/hOv?YAl/hx?_"p?_"ykx?_"ykfi_\Aykx Xg_io Ykn?Xgfi_ fiY(ykol9X \8j}yEl o&hkjmfih]^\A¦8_ l9hk_p?XgY(vkqm_"] WºÍfiY(]^pkqs_il_&j}y^[A_"yk_"X \8qG
(35) > Y(yko jmx?_"Xl9hk_ GYAqmqsY8j}yk[ _i{?\A]pkqm_l YOjmqmq}nko l9X \8l_Ql/hk_x?jsof"nko o jmY(y O_£jmqsq Y(X¦Y(y¨l/hkjso-_i{?\A]pkqm_Q\8qmq\8qmY(yk[§l9hk_ p?\Ap_"Xi. *? @
(36)
(37) A !â² CBEDGFIH:JK LMON PRQ D 'FTS"UDCVK` LMW PRX"UD =FTQ D%V§" ZY\[ UDCVK` LM:] PR"S UD =FT"X UD +^ ` LM:_ PR[ D `FTa D%V ` cAb LMd PRe D 'F o j}y a DC§ V " LMf PRa D 'F qsYE[ "X UD ^ge D h CB < hk_¡j}yko l9Xnkfil jmY(yko ULM N Ji/iic#J LM:j jml9hkj}y l/hk_qsYkY(p klF «j}y°Y(n?X,_i{?\A]pkqm_ \EXg_ f"\8qmqm_ix
(38) m noqpr" %)-/ "sut Oh \8fih£Y8 l9hk_"] jmo0_i{(_if"nkl _ixvKw^ `,l j}],_io"u
(39) hk_"Xg_ K jmo\8oo9n?],_ixl Yv?_,¢A_"Xg|q}\AXg[E_A+çx yko l9\Aykfi_y D Y8Y(p_"X \8l jmY(yzLM:{jmox?_"ykYAl _ix LM:{(JD iuR\Aykx jml o_i{k_if"nkl jmY(y£jmoo fhk_ix nkqm_ix§l Yv_i[Aj}yO\8l l j}],_}| LM:{uJD ~TH \Aykxl Yq}\8ol LM:{ n?ykjml oY8 l j}],_A < hk_[AY(\8q jmo¡l Y§x?_il _"X ],j}yk_¨\Oofhk_ix nkqm_| l Y] jykj}],j3i _¨l9hk_l YEl9\8q_i{k_if"nkl jmY(y l j}],_ lF ]\8{ | ULMs{JD ^g LM:{ ;J `#TTk=JH}TDTK o9n?vk~g_ifil&lY (" ( % ": ( " $ u \Aykx£&hkjmqm_ap?Xg_io _"XZ¢(j}yk[-l9hk_o _"]^\AyAljsfio#Y8 l/hk_Y(Xgjm[Aj}y?\8q
(40) qmYkY(p ()-/"/ C ": ( "$$ i ^²÷'¶
(41) 88²O8¶
(42) i";U " çx yl9hk_,],YAo l [A_"yk_"X \rq
(43) j}yko l9\Aykfi_0Y8 l/hk_C8:9 p?XgY(vkqm_"]uXg_io Ykn?Xgfi_ fiY(ykol9X \8j}yEl o\AXg_-_i{÷p?Xg_ioo _ix \8oGYAqmqmY8oP [A_"yk_"Xgjmfl9\8o/¦Ao,\AXg_p?\AXgl jml jmY(yk_ix¨j}yEl Yfiq\ro o _io"'%< Y _"\8fih¨fiq}\8oo}) fiY(X XZ_io9p?Y(ykx?o¡\[Ajm¢A_"y w ykjml _ -ykn?]av_"XCM ,Y8\"¢8\8jmq}\Avkqm_p?XZY(fi_io oY(Xgo 6Y(X Xg_ioY(n?Xgfi_io i®RY(X,_i{?\A]pkqm_l9hkj}y?¦§Y8&l9\ro9¦Aov_ijyk[¨p?\AXgljsljsYkyk_ix¨jyEl Y \rx?x?jsljsYkyko 6fiq}\8oo% N \Aykx)],nkqml j}pkqmjsf"\rl jmY(yko 6fiq}\8o omW l9hk_"yv M ON ^jmol9hk_Oy(n?],v?_"X-Yra\"¢8\8jmq}\Avkqm_\8x?x?_"XZo¡\Aykx M sW l9h?\8lY8&],nkqml j}pkqmjs_"XZo"O_yk_i_ix§l Y_"yko9n?XZ_l9h?\rll9hk_o fihk_ix nkqmjyk[§| o9\8ljso& _iol Y£l9hk_ Xg_ioY(n?Xgfi_fiY(ykol9X \8j}yEl o"u;jM _A8l9h?\8l\8l\AyE|l j}],_/ºÍo l_"p\Aykx,GY(X%_"\8fh^Xg_io Y(n?Xgfi_ fiq}\8o o uðykY],YkXg_ l9h?\Ey% M jykol9\Aykfi_io Y8 l/\8o9¦Eo&v?_iqmY(yk[Aj}yk[-l Yfiq}\8o o © \EXg_v?_ij}yk[_i{k_if"nkl _ix
(44) Íx y\ o j}]pkqm_"X¯jykol9\Aykfi_Y8l9hk_8:O 9 p?XgY(vkqm_"]uEl9hk_"Xg_ jmo\ o j}yk[Aqm_cXZ_io Y(n?Xgfi_ fiq}\8o ofiY(]^p?YAo _ix Y8§ M jmx?_"yAl jmf"\8qp?XgYkfi_io o Y(XZo"'h \8fihOYkp?_"X \8ljsYkyL°M f"\Ay v_¡_i{k_if"nkl _ix¨j}ykx?j _"XZ_"yAl qm|KY(y \EyA| Ü
(45) Ü ×! ü.
(46) . ".$.3 " =
(47) " .
(48) .
(49) 2 . p?XgYkfi_io o YkXiuAjml9h x?_iq\;|} LM i8d qml9hkY(nk[(h^qm_io o[A_"yk_"X\8qGuAl9hkjmo o j}yk[Aqm_cXZ_io Y(n?Xgfi_fiq}\8ooj}yko l9\Aykfi_ h?\8o ],YAl jm¢ð\rl _ixQ\,[kXg_"\8l x?_"\8q
(50) Y8Xg_io _"\EXgfhuEGY(X\8l qm_"\8o l lg Y XZ_"\8o Y(ykoP jml h?\roa\[kXg_"\8lj}]p?YkXgl9\Aykfi_-j}y p?X \rfil jmfi_Au \rojsl],Ykx?_iqmo wyk_/ºÍ[(X \8j}y§p?\AX \8qmqm_iqmjso/] _i{Eº l9X \8filjsYky jy0o9h?\EXg_ixa],_"] Y(Xg|]\8fihkjyk_iojml9h0p?XgYA[(X \E]]\Avkqm_d o MY(XRnY ºÍl9hk_/ºÍo9hk_iq» ],jmf"XgY(p?XgYkfi_io o YkXgo iu jmljmol9hk_-Y(ykqm| f"\8o_&hk_"Xg_[(n?\AX\AyAl_i_io_i{kjsol¡ª¬«' MY(X0o fihk_ix nkqmj}yk[ hk_"n?Xgjmo l jmfio" <hkjmo jmo¢A_"Xg|-j]^p?Y(Xgl/\AyAl\8ojml[Ajm¢A_io\^o Y(n?ykxQv?\ro jmoGY(X#fiY(]p?\AXgj}yk[hk_"n?Xgjmo l jmfioMl9hk_Y(ykqm| \8qml _"X y?\8ljs¢E_jso l Y],nkqml j}pkqm|¡_i{?p?_"Xgj}],_"yEl o ' -²:A²
(51) ·%²
(52) 8²¤8¶
(53) i";U " _"p_"ykx?_"ykfi_¨fiY(yko l9X\8j}yAl o£_i{÷p?XZ_io o¡l9hk_ \8fil£l9h?\8lo Yk],_. fiY(]^p?nkl9\8l jmY(yko],nko lv?__i{k_if"nkl _ix£jy£\,o9p_ifij _ix©Y(Xgx?_"X o Y-\8o l Yp?Xg_io _"XZ¢A_l9hk_o_"]\AyEl jmfio Y8
(54) l9hk_ qmY(Ykp- xçyYkn?X_i{?\A]pkqm_AukfiY(]p?nkl9\8ljsYky LMONJD &Xgjml _io Q D iuAhk_"ykfi_jml],nko l p?Xg_ifi_ix?_ fiY(]^p?nkl9\8l jmY(y LMW/JD ^¨" &hkjmfih¡Xg_"\8x?o#l9hkjmo&¢8\8q}nk_A <hk_"Xg_0jso \8qmo Y G\A] Y(yk[,YAl9hk_"Xgo #\x?_/º p_"ykx?_"ykfi_ÍXgY(] U LM f JDV" l Y LMdJD iuAv?_if"\AnkoC _ a U D#V" ]ankol v?_Xg_"\8x-j}y LMdJD iAd qmq x?_"p_"ykx?_"ykfi_ioa\AXg_nko/n?\8qmqs|f"\Epkl9n?Xg_ix¡j}yEl Y\XZ_ix nkfi_ix¡x?_"p?_"ykx?_"ykfi_^[(X \Ap?h 6o_i_®js[kn?Xg_` ' <hk_ 8:9¨p?XZY(vkqm_"]¤h?\8o],YAl jm¢8\8l _ix\[kXg_"\8l \E],Y(n?yElY8¹Xg_io _"\EXgfh?¸kj}ykfi_l9hk_pkjmY(yk_i_"Xgj}yk[ Y(X ¦^Y8d j}N ¦8_"y\Aykx #j}¦8YAq}\An§ª}`=u?o _i¢E_"X \8q\Ankl9hkY(Xgo h?\"¢E_ap?XgY(pYAo _ix£¢ð\AXgjmY(nkohk_"n?Xgjmo l jmfio-ª¬«ku ?uR?u? ?u ; <hk_]\8j}y fiY(yAl/Xgj}v?nkl jmY(yY8l9hkjmocp?\Ap_"XjmolYp?Xg_io _"yEl|A_il&\EykYAl9hk_"X hk_"n?Xgjmo l jmf GY(X l9hky _ 8:9 p?XgY(vkqm_"]%O_v_iqsjm_i¢A_l/hkjso,hk_"n?Xgjmo l jmf-l Y¡v?_Yrj}yEl _"Xg_io lv_if"\Anko _-jmlav?Xgj}yk[Ao,\ yk_i j}yko jm[(hEll Y0l9hk_ 8:9§p?XgY(vkqm_"]+vA|,_io l9\Evkqsjmo9hkj}yk[jml ox?_i_"pqmj}y?¦,jml9h^l9hk_fij}Xgf"nkjmlXg_il j}],j}yk[ p?XgYkvkqs_"] Ad qsoY u8j}y,l9hk_ o j}yk[Aqm_&Xg_io Ykn?Xgfi_ fiq\ro of"\8o_Au"Y(n?Xyk_i hk_"n?XZjsol jmf&jmo[(n?\AX\AyAl_i_ix
(55) u8jml9h \,v?_ill _"Xv?Ykn?ykxl9h?\Ay-l9h?\8lY8 ª¬«ð=A®j}y?\8qmqm|Au _p?YAj}yElY(nkl l9h?\8l;uAj}yjml o o j}]pkqm_io l#MYkX ]uAYkn?X \8qm[AYkXgjml9h?] h?\ro&\,qmY8 _"XfiY(]^pkqs_i{kjmlg|A <hk_ Xg_io lYr l/hk_p?\Ep?_"X£jmo¡Y(Xg[k\Ayk3j i_ix$\8o-GYAqmqsY8/o Pj}y)¸k_ifil jmY(y ?u _£MY(X]\8qmqm| x?_/º wyk_l9hk_ 8:9 p?XgY(vkqm_"] \Aykx§ _ v?Xgjm_ |§o9n?Xg¢A_i|fiY(]^pkqs_i{kjmlg|Xg_io/nkqslo \Eykxhk_"n?Xgjmo ljsfio^ÍXgY(] l9hk_^qsjml _"X\8l9n?Xg_A' xÍy©¸k_ifil jmY(y u _-p?Xg_io _"yEll9hk_[kn?\AX \AyEl _i_ixOhk_"n?Xgjmo l jmfY8 \8o9p_"XgY(ykj \Aykx ¸kfihA#js_i[E_iqso/hkY(h?y)ª¬«'=` xÍy§¸k_ifil jmY(y§?¬?u% _^o9hkY8 hkY8 l Y],Ykx?j¬G|Ol9hkjmohk_"n?Xgjmo l jmfo Y\8o,l Y f"nkl],Y(XZ__ix?[A_ioj}y^l9hk_ x?_"p?_"ykx?_"ykfi_[kX \Ap?h Ghk_"ykfi_ _i{?p?_ifil j}yk[v?_il l_"X XZ_io9nkqml o i <hkjmo [Ejs¢E_io l9hk_ol9\AXgl j}yk[p?YEjyElY8Y(n?X hk_"n?Xgjmo l jmf0&hkYAo _p?Xg_io_"yAl9\rl jmY(y-jmoo9pkqmjml&Y8¢A_"X ¸k_ifil jmY(yko \Aykx¡? ®n?Xgl9hk_"X ],YkXg_Au _-o9hkY8+l9h?\8l,l9hk_v?Y(n?ykx°MYkXY(n?Xhk_"n?XZjsol jmf¡jmov?_ill _"X0l9h?\Ay©l9hk_¡v?Y(n?ykx j}yKª¬«'=®j}y?\8qmqs|Au _,x?jmo f"nko o,o Y(],_,_i{kl _"yko jmY(yko0jy©¸k_ifil jmY(y «O_,o9n?]]\AXZ0j i_^Y(n?XXg_io/nkqslo \Aykx£[Ajm¢A_o Y(] _p?_"Xgo9p_ifil jm¢A_ioj}y¡¸k_ifil jmY(y£ ? ó;æ¬Õ
(56) ÕGÙ ë ìíì?ìíæ¬ÕGÏ%æ¬ Õ }ëË mËÍÌ9Ù§öAÉçæí×ðòØgÌ/ÙÊ"ËÍÉçóðÉç×ðÕ6æ¬ê/É/ä. áâÛ¹Üá}ã.
(57)
(58)
(59) !" #$ %!& !' " (*)+,)-/.0$$"1)+ (
(60) 2.3/4 6 op4. 1 2. 4 op 2. 1 op1 1. 1 0. 0 op3 2. 14 op6 0. 2 10 op5. ®jm[(n?Xg_`P<hk_Xg_ix nkfi_ix£x?_"p?_"ykx?_"ykfi_[(X\Ap?h . ! %.Zw !
(61)
(62) . *0
(63) !&1,. 2. ®RY(X ]\8qmqm|AuRo Y8Gl=\AXZ_cpkj}p?_iqmj}y?j}yk[Op?XgY(vkqm_"] j}yko l9\Eykfi_ioc\AXZ_aXg_"p?Xg_io_"yAl _ixvA|¡\ wykjml _AuR¢A_"Xgl _i{Eº _ijm[(hEl _ix
(64) uA_ix?[A_/ºÍ _ijm[(hEl _ix-x?jXZ_ifil _ix¡],nkqslj¬ºÍ[kX \Ap?hlF "!J$#yJc/J[ /<hk_ ¢A_"Xgl jmfi_io%! Y8
(65) l9hk_ [(X\Ap?h],Ykx?_iq
(66) l9hk_[E_"yk_"Xgjmfl9\8o/¦Ao P&! F LMONJLMWJi/iicJLM j (:h\8fih-[A_"yk_"Xgjmf,l9\8o9¦LMs{ h?\8o \ pYAo jml jm¢A_-x?_iq\;| 6Y(X#q}\8l _"ykfi| C LM:{ '( '_"Xgl _i{ 6l9\8o/¦ #x?_iq}\"|kC o -f"\Ayv?_-X \8l jmY(y?\8qykn?],v?_"Xgo;u v?nklojykfi_£l9hk_[(X \Ep?h§jso wykjsl_¡ _f"\Ay¨\8qm\;|(o,fih?\Ayk[A_l9hk_l j}],_¡n?ykjml-l YOh?\;¢A_j}yAl _i[E_"X x?_iq}\;|(o;+ <hk_[kX \Ap?) h jmo Y8Gl _"yf"\rqsqm_ixl9hk_ " }"&)-/"/
(67) ( ) j}yl/hk_qsjml _"X\8l9n?Xg_A h\8fih[A_"yk_"XZjsf,l9\ro9y¦ LM:{h?\8o o _i¢A_"X \rq
(68) j}yko l9\Aykfi_io LM:{rJD iu HTD TK§ <hk_,p?XgY(vkqm_"]¤jmo l 1Y wykx¡\o fihk_ix nkqmC_ |£l9h?\8l\8o ojs[kyko\l j}],_/ºÍo l _"p | LM:{uJD lYav?_i[Ejy-l/hk_&_i{k_if"nkl jmY(y-Y8
(69) _"\8fih fiY(]^p?nkl9\8l jmY(y LM { JD ' <hk_ x?j}Xg_ifil_ix _ix?[A_i*o # Y8l9hk_§[(X \Ap?h ],Y(x?_iq,x?_"p_"ykx?_"ykfi_ fiY(yko l/X \8j}yAlo" _il e F LM:{(JLM+ * ,-# v_\Ey¨_ix?[A_£Y8. jml9h¨ _ijm[(hEl [ e Pl9hkjmo¡],_"\Ayko-l9h?\8lj}yko l/\Aykfi_ D¨Y8 [A_"yk_"XZjsfl9\ro9 ¦ LM:{c],nko lv?_£fiY(]pkqm_il _ix)v?_/GY(Xg_£l9hk_¡_i{k_if"nkl jmY(y Yrcj}yko l9\Eykfi_ Dm^ [ e ,Y8 [A_"yk_"XZjsf,l9\ro9} ¦ LM+8 xÍy YAl9hk_"X Y(XZx?o"uk _h?\;¢A_l/hk_o fhk_ix nkqmj}yk[fiY(yko l/X \8j}yAlo P / e F LM:{rJLM+ % ,0#EP"| LM:{uJD + ^ LM:{ g| U LM1+JD ^ [ U e h¯x?[A_¡x?_iq}\;|(o¡\EXg_¡ykY(y?yk_i[(\8ljs¢E_Qj}yEl _i[A_"XgovE|¨fiY(yko l9X nkfiljsYky¸kY(],_£_ix?[A_x?_iq\;|ko ]^\"|¨v?_ _ ?n?\8q
(70) l % Y i_"XgYRu v?nkll9hk_"Xg_x?Yk_ioykYAl _i{(jmo l\AyE|fi|(fiqm_0j2 y &hkYEo _qm_"yk[Al9h 6l9hk_o/n?]+Y8l9hk_ _ix?[A_,x?_iq}\;|(o jm#o i_"XgY 6YAl/hk_"Xgjmo _oY(],_fiYk]p?nkl9\8l jmY(y-x?_"p_"ykx?oan?pY(yjml o _iq» '+ <hk_,],nkqslj¬º [(X\Ap?3 h GY(XY(n?X¯_i{÷\E]pkqm_&jmox?_"pkjmfil _ixj}y^®js[kn?Xg_a` PAY(p_"X \8l Y(Xx?_iq}\;|ko\EXg_&[Ejs¢E_"yj}y^o ÷n?\EXg_ vYð{k_io" _io Y(n?Xgfi_0fiY(yko l9X\8j}yAl o \AXg__i{?p?Xg_io o _ixO\8o GYAqmqmY8o P?[A_"yk_"XZjsf,l9\ro9¦Ao\AXZ_ap?\AXgljsljsYkyk_ix¡j}yAlY fiq}\8o o_io" <%Y_"\8fihfiq}\8o o fiYkX Xg_io9pY(ykx?o&\0[Ajm¢A_"yykn?]av_"'X M Y8 \;¢8\8jmq\Evkqs_,p?XgYkfi_io o Y(Xgo 6Y(X Xg_ioY(n?Xgfi_io i%O_yk_i_ix l Y£_"yko9n?Xg_l9h?\rl\8la\AyE|Ol j}],_/ºÍol _"p ykY],Y(Xg_^l9h?\A y M j}yko l9\Aykfi_io Y8 l9\8o9¦Eo&v_iqsYkyk[Aj}yk[QlYfiq}\8o o ¨\AXg_av_ij}yk[¡_i{k_if"nkl _ix
(71) <hkjmol9X\Ayko q}\8l _io j}yAl Y-l9hk_0GYAqmqsY8j}yk[ Ü
(72) Ü ×! ü.
(73) «. . ".$.3 " =
(74) " .
(75) .
(76) 2 . GY(X ],nkq}\:P. / ~gHsJ / J LMJcD JcLM3,m JH gD KqJ V LM g| ULMZJD ' :M i. _io Y(n?Xgfi_ fiY(yko l/X \8j}yAlof"\Ayv?_#_i{÷p?Xg_ioo _ixoqsjm[(hEl qm|x?j
(77) _"Xg_"yEl qm|j}y,l9hk_f"\8o_Y8pkj}p_iqsj}yk_;x ?p XgYkfi_io o YkXgo"=xM _-\8o o9n?],_-p?XgY(fi_ioo Y(Xgo0Y8 fiq}\8o o ¨l YQv_ pkj}p_iqsj}yk_ix
(78) ul9hk_"yOykY],Y(Xg_l/h?\Ay M l9\ro9¦Ao#Y8 fiq}\8ooOf"\Ayv?_0jykjml j}\8l_ix\rl _"\rfh£n?ykjsl Y8¹lj] _A <hkG_ 8:9)p?XZY(vkqm_"] f"\Ayl9hk_"XZ_/MY(XZ_av?_Xg_ix nkfi_ix©l Yl9hk_,x?_il _"X ] jy?\rl jmY(y£Y8l9hk_ofhk_ix nkqm_ | o/n?vk~=_ifil,l Yl9hk_¡\Ev?Y8¢A_-fiY(yko l9X \rjyEl o" ".3 o fihk_ix nkqm_io \AXZ_l9hkYEo _ofhk_ix nkqm_ioo9\8ljsoZM|kj}yk[ \8qmqfiY(yko l9X \rjyEl o GvYAl9h£x?_"p?_"ykx?_"ykfi_fiYkyko l9X \8j}yEl o\AykxOXg_io Ykn?Xgfi_fiY(yko l/X \8j}yAlo i _if"\Enko _Y8 l9hk_Xg_i[knkq\EX o l9X nkfil9n?XZ_Y8 l9hkG _ 8:9)p?XZY(vkqm_"]u _ nko/n?\8qmqs|o _"\EXgfh MYkX&\
(79) n .3$ o fhk_ix nkqm_ |'P _\8j}]¥\8l wykx?j}yk[\£ykY(y?yk_i[(\8ljs¢E_j}yAl _i[E_" X 6f"\8qmqm_ix $
(80) $$$ " $/ / ". Yr* | \Aykx fiY(ykol9\AyEl o S{
(81) o9nkfihl/h?\8l | LM { JD ' F sD ^gS { _if"\Enko _l9hk_jy?p?nkl£qmY(Y(pKjmoo9n?p?pYAo _ix l Y§_i{(_if"nkl _§]\AyE|¨jsl_"X \8l jmY(yko Kjmo¡q}\AXZ[A_ iu _GYkf"nkoY(y°l9hk_¡\8o |?]pkl YEl jmfQv?_"h?\;¢kjmY(XYrG |' <hk_¡j}ykjml j}\8l jmY(y j}yEl _"Xg¢8\8 q ¨jmo\ y?\8l/n?X \8q p_"XçMYkX ]\Aykfi__io l j}]\8l YkX Yrs |u;\8o` b ],_"\8o9n?XZ_i=o | ío
(82) l/h?XgY(nk[(h?p?nkl" YAl_l9h?\8lj» l9hk_ Xg_ix nkfi_ix x?_"p_"ykx?_"ykfi_[(X \Ap?h )jmo \rfi|(fiqmjmf&\Aykxj»l9hk_ l9\AXg[A_il]\8fihkj}yk_&h?\8o_"ykY(nk[khp?XgYkfi_io o Y(Xgo;u8l9hk_"y f"\AyvC _ i_"XgY Ml9hkjmo&lg|?p?_Y8o fihk_ix nkqs_h?\8o#jy wykjml _,l9h?XZY(nk[(h?p?nkl i d¤¢ð\AXZj\EyAl,fiY(yko jmo loj}y§o _"\AXgfihkj}yk[MYkX\ykY(y?yk_i[(\8ljs¢E_¡X \8l jmY(y?\8q Fb\Aykx¨l Y¡qm_il | U LMs{uJD ' F D#^ S{ 6jml9h£X \8l jmY(y?\8qfiY(ykol9\AyEl o S{ i: <hkjmo\A],Y(n?yEl o l Yn?y?XZYAqmq¹l9hk_j}y?p?nkl qmYkY(pOvE|Q\ \8filY( X R#YAl _l/h?\8lcX\8l jmY(y?\8qfi|kfiqmjsf^o fhk_ix nkqm_io\AXg_0x?Y(],j}y?\AyElj}yl9hk_,f"\8o _,Y8 n?ykqmj}],jml _ix Xg_ioY(n?Xgfi_ioª¬'= xÍy©l9hk_,GYAqmqsY8j}yk[ u _Xg_iol9Xgjmfill Y£l9hk_o j}]pkqm_io l^f"\8o _Au
(83) jGí_A%l9hk_-f"\8o _Y8 U !}² "²k´ '¶
(84) ðr² !} ;¡YrG ¶ A`$A² $! ²?· A;¶r²÷;i¶w8E Bn?X-hk_"n?Xgjmo l jmfx?Yk_io\Ap?pkqm| l YO]\EyA| Xg_ioY(n?Xgfi_fiq}\8oo _io"u v?nkl _\AXZ_ykYqmY(yk[A_"X \Avkqm_l Y,[(n?\AX\AyAl_i_jsl#jy l9hkjmo&f"\ro _A. . !#" $. O\AyE|Op?\Ap?_"Xgo,Y(yo Y8Gl=\AXZ_apkj}p?_iqmj}ykjFyk[¨h?\"¢E_v?_i_"y¨p?n?vkqmjmo9hk_ix
(85) xçyOl9hkjmo,o _ifil jmY(yu% _¢A_"Xg| v?Xgjm_ |¨o9n?]^]\AXg3j i_^MY(n?X0Y8 l9hk_¡],YAo l,Xg_ifi_"yElaYkyk_io"uvA|O®R_"\Ankl9Xgjm_"Xª»igu&% \Ayk_"y§\Aykx¨OnEº ykjm_"X0ª¬;=u \ro9p?_"XgYkykj¹\Aykx¡¸kfihAjm_i[A_iqmo9hkYkh?y ª»«i\Aykx¡ \Eyk[a_il \8qG¹ª '= '%²( "n }²?) (+*, ® _"\Enkl9Xgjm_"X GY(X ]^\8qm0j i_io l9hkC _ 8:9 p?XgY(vkqm_"] j}yl _"X ] oY8jyEl _i[A_"Xqsj}yk_"\AXp?XZY8º [(X\A]],j}yk[ uj}y§l9hk_-f"\8o _Y8x?j
(86) _"Xg_"yAl-Xg_io Y(n?Xgfi_-fiq}\8o o _io;-%_-[Ajm¢A_iolg Y¡ofhk_ix nkqmj}yk[\rqs[EY8º Xgjml9h?] o"u Ykyk_ MY(Xl9hk_f"\8o _ M = F` 6 hkjsfih¡] _"\Aykol9h?\8l \8qmq¹Xg_io Y(n?XZfi_io&\AXg_fiY(ykojsx?_"XZ_ix\ro x?j
(87) _"Xg_"yEl &\Eykx¡\AykYAl9hk_"XGY(X l/hk_[A_"yk_"X \8q
(88) f"\ro _A xÍyvYAl9h f"\8o _io"u?jmljmo o9hkY8&yhkY8)l Y,l9X \Eykogº q}\8l _XZ_io Y(n?Xgfi_ fiY(yko l9X\8j}yAl o j}yEl Y,o |(ol _"],o Y8 vkjmqmj}yk_"\AX j}yAl _i[E_"XfiYkyko l9X \8j}yEl o": <hkjmol _ifih?ykj÷nk_ p_"X ],jml o l Yx?_"Xgjm¢A_0Y(pkl j}]\8qo YAq}nkl jmY(yko;u l9hkYknk[(h-j}y¡ykY(yEº=pYAqm|÷ykY(] j\rq¹l j}],_A. áâÛ¹Üá}ã.
(89)
(90)
(91) !" #$ %!& !' " (*)+,)-/.0$$"1)+ (
(92) 2.3/4 Ow²$O
(93) · =â²÷ ( , % \Ayk_"y§\AykxOOn?ykjm_"X,nko _ \ ¢A_"Xg|j}yAl_"Xg_io l j}yk[[(X \Ap?hEº=v?\ro _ix \Ap?p?XZY(\8fih<hk_i|¡Xg_io l/Xgjmfil&l9hk_"] o _iqm¢A_io&lYl9hk_ojyk[Eqs_Xg_ioY(n?Xgfi_fiq}\8o o f"\8o _AO<hk_i|¡nko _ l jm_/º v?Xg_"\E¦Aj}yk[ O[kX \Ap?hko,l Yx?_"Xgjm¢A_o fihk_ix nkqm_io" \8ojsf"\rqsqm|Aul9hk_jmx?_"\jmol YO\8x?x¨o Yk],__ix?[E_iol Y l9hk_,Xg_ix nkfi_ix¡x?_"p_"ykx?_"ykfi_[(X \Ep?h <hk_io _,yk_i)_ix?[A_io qsj}y?¦ l9\8o9¦,j}yko l/\Aykfi_io&lYv?_0_i{(_if"nkl _ix Y(yKl9hk_£o9\A],_£[(XgY(n?p°Y8ap?XgYkfi_io o Y(XZo"\ <#hk_Qp?XgY(vkqm_"] jmol Y§x?_il _"X ],j}yk_OhkY8 lYp?\AXZl jml jmY(y p?XgYkfi_io o YkXgoj}yEl Y§[(XgY(n?pko\Aykx hkY8 l Y \8x?x yk_i _ix?[E_io"\ <#hk_p?XZY(p?YAo_ix hk_"n?Xgjmo l jmfio£qsYkY(¦ ?nkjml _apYð _"XçÍnkqGu \8qml9hkY(nk[kh¡ykYAl[kn?\AX \AyEl _i_ix
(94) . . . . - A²?"¶Z #O
(95) ·
(96) µyâ² R² !6 ¶ `( , 0\8o9p_"XgY(ykj\AykxO¸kfhEjm_i[A_iqmo9hkY(h?yl/\8f¦Eqm_,l9hk_ o j}yk[Aqm_Xg_io Y(n?XZfi_fiq}\8o of"\ro _Au
(97) v?YAl/hjml9hOpkj}p?_iqmj}yk_ix \EykxykYkyEº=pkjp_iqmjFyk_ix p?XgYkfi_io o YkXgo"<hk_i| nko _-|A_il\AykYEl9hk_"X\Ap?p?XZY(\8fiOh Pl9hk_i|o _"p?\AX \8l_Auo Y¡l Yo/p?_"\A¦Ru
(98) x?_"p_"ykx?_"ykfi_fiY(yko l9X \rjyEl o,\Aykx Xg_ioY(n?Xgfi_ fiY(yko l9X \rjyEl o" <hk_i% | wXgol ofhk_ix nkqm_l9hk_Xg_ix nkfi_ixx?_"p?_"ykx?_"ykfi_,[(X\Ap? h \8o o/n?],j}yk[ \AyKn?ykqmj] jsl_ix ykn?],v?_"X^Y8p?XgY(fi_ioo Y(Xgo"¸?nkfih \ofhk_ix nkqm_jmol9hk_¡v?\ro jmol Yx?_ifijmx?_&hkjmfh _ix?[A_iolYf"nkljy ¤oY \8olY ]\E¦8_jml\8fi|kfiqmjsfA` Byl9hk_,yk_i \8fi|kfiqmjsf^[(X \Ap?2 h 8ul9hk_i|nko _ \£qmjmo lgºÍo fihk_ix nkqmjy[ hk_"n?Xgjmo l jmf¡lY¡fiY(p_jml9h§l9hk_Xg_io Y(n?Xgfi_fiYkyko l9X \8j}yEl o"` <hk_¡¦8_i|Eº=p?YAj}yElajmo l9h?\rll9hk*_ wy?\8qo fihk_ix nkqsj}yk[jmo[kn?\AX \AyEl _i_ix
(99) 8O_ _i{÷pkq}\8j}y \8o9p_"XgY(ykj\Aykx ¸kfihEjm_i[A_iqmo9hkY(h?y ío \Ap?p?XZY(\8fih-jml9h-Ínkqmq
(100) x?_il9\8jmqmo&j}y¸k_ifil jmY(y£?u?\Aykx¡ _v?nkjsqmx n?pY(y-l9hk_ij}X Xg_io9nkqml o" .
(101) . . . . . O O? 6i²w²:F ¶ 8·%OQO
(102) · ( , \Eyk[_il\8qGAh?\"¢E_\Eya\Ep?p?XgY(\8fih0¢A_"Xg|oj] j¬º q}\AXl Y,l9h?\8lY8 0\8o9p?_"XZY(ykjw\Aykx¸kfihAjm_i[A_iqmo9hkYkh?y<hk_]\8j}y^x?j_"XZ_"ykfi_jso#jy^l9hk_ o _iqm_ifil jmY(y f"Xgjml _"XZjsYky,l Yf"nkl_ix?[A_ioj}y o Y\8olYc]\E¦8_jml \rfi|(fiqmjmfA
(103) <hk_i|0f"nkl],Y(Xg_ _ix?[A_iol/h?\Ay \8o9p_/º XgYkykj \AykxO¸kfihA#js_i[E_iqso/hkY(h?yul9hk_"Xg_"vE|¡_i{?p?_ifil j}yk[¡v_il l _"XXg_io9nkqml o hk_"yqmjmo lgºÍo fihk_ix nkqmjFyk[l9hk_ \8fi|kfiqmjmfa[kX \Ap?) h 8 . .
(104) . . . . ® Y(XYkn?X¹yk_i hk_"n?Xgjmo ljsfAu8 _ \Ap?pkqm|l9hkjmojsx?_"\ Yr÷f"nkl ljyk[_ix?[E_io¹l YkY Bn?X[EY(\8qAjmol= Y8GYAqmxP j] jyk3j i_§l9hk_qmY(yk[A_io lp?\8l9hKj}y l9hk_\8fi|(fiqmjmf§[(X \Ap?h £o Y¨\8olYh?\;¢A_l9hk_Ov?_iol p?YAoo j}vkqs_p_"XçMYkX ]\Aykfi_vY(n?ykx
(105) uwhk_"ykfi_0j}]p?XgY8¢(j}yk[-l9hk_hk_"n?Xgjmo l jmf,[(n?\AX\AyAl_i_Au jykj}],3j i_l/hk_ ykn?]av_"X
(106) Yr÷_ix?[A_ioj}y oY&\8ol Y&h?\;¢A_\8o%M_i§fiY(yko l/X \8j}yAlo¹\8o¹pYAo o j}vkqm_A d oa\8q}Xg_"\rx?|Q],_"yEl jmY(yk_ix
(107) u
(108) _ wXgo lx?_iof"Xgj}v?_ \8o9p_"XgY(ykj\Aykx ¸kfihA#js_i[E_iqso/hkY(h?y íoa\Ep?p?XgY(\8fih G¸k_ifiljsYky¡" v_/MYkXg_j}yAl9XZY(x nkfij}yk[Y(n?Xyk_i hk_"n?Xgjmo l jmf G¸k_ifil jmY(y¡¬" i . . . . !& ' !2. . ^. / ! . . . . _/GY(Xg_¡[EYAj}yk[¨jyEl Y§l9hk_¡x?_il/\8jmqsoYr \8o9p_"XgY(ykj&\Eykx ¸kfihAjm_i[A_iqmo9hkYkh?y)hk_"n?Xgjmo l jmf 0¸§GY(X o9hkYkXgl iu _Xg_if"\8qmqo Y(] _p?XgY(p_"Xgl jm_ioY8 fi|(fiqmjmf-o fhk_ix nkqm_io"uo Y¡\rol Y¡]\A¦8_,l9hk_-Xg_io lY8 l9hk_ p?Xg_io_"yAl9\rl jmY(yfiqm_"\AXg_"X'. Ü
(109) Ü ×! ü.
(110) . . . ".$.3 " =
(111) " .
(112) .
(113) 2 . &
(114) ! js¢E_"yl9hk_ x?_"p?_"ykx?_"ykfi_0[(X \Ap?h lF "! J$y # Jc/J[ /u"\fi|kfiqmjmfo fihk_ix nkqm_C|jmo\o fihk_ix nkqm_Y8
(115) l9hk_ GY(X ] P | LM:{uJD `F D#^S{&hk_"Xg_ JS{JD2, . l9h?\rlao/\8l jmo( _iov?YAl/hOx?_"p_"ykx?_"ykfi_¡fiY(yko l/X \8j}yAlo \EykxXg_ioY(n?Xgfi_-fiY(yko l9X \rjyEl o"¸?nkfh§\£fi|(fiqmjmf o fihk_ix nkqm_jmop?_"XgjmYkx?jmfAu
(116) jml9hp?_"XZjsYkx P l9hk_0fiY(]p?nkl9\rl jmY(yo fihk_"],_,jmoXg_"p?XgYkx nkfi_ix_i¢A_"Xg| n?ykjml o Y8¹l j}],_AkY(Xg_p?Xg_ifijmo _iqm|Auj» j}yko l/\Aykfi_ LM:{uJD jmo&\ro o jm[(yk_ixl Yv?_i[Ejy£\8l l j}],_ ul9hk_"y j}yko l9\Eykfi_ LM:{uJD^§` jmqmq
(117) v?_i[Aj}y\8ll j}],_ ^
(118) - <#hk_"Xg_/MYkXg_ _&Ykykqs|-yk_i_ixl Yo l/nkx?|\o qmjmfi_ Y8 ,fiqmY(fi¦,fi|kfiqs_io l Y,¦(ykY8¨l9hk_ v?_"h?\;¢(jmY(XY8l9hk_&hkYEqs_ fi|kfiqsjmfo fihk_ix nkqmj}yk[j}y,o l _"\8x?|,o l/\8l _A. op (k) 1. op1(k+1). time. op2(k). op4(k-1) op (k) 5 op (k-1) 6. op3(k). op2(k+1) op (k+1) 3. op4(k) op (k) 6 op (k+1) 5. op (k+1) 6. processors. ®jm[(n?Xg_ :PA¸?nkfifi_io o jm¢A_ o qmjmfi_io Yr%\ ofhk_ix nkqm_#MY(X[kX \Ap?h n?y(v?XgYk¦8_"y,qmj}yk_ioXZ_"p?Xg_io _"yEll=|?p?_0` x?_"p_"ykx?_"ykfi_io"u
(119) x?YAll _ixqmjyk_ioXg_"p?Xg_io_"yAl lg|÷p_,x?_"p?_"ykx?_"ykfi_io ' _ilnkoaYkvko _"Xg¢A_o/nkfh§\o qmjmfi_Au_Aí[R
(120) l9hk_-o qmjmfi _ XZY(] fiqmYkf¦fi|kfiqm_ n?pOl Y£fiqmY(fi¦ fi|kfiqm_ ^ ` V©`AuA&hk_"XZ_ jmo q\EXg[A__"ykY(nk[(h^o Y,l9h?\8ll9hk_o l _"\rx?|aol9\8l _ jmoXZ_"\8fhk_ix Mo _i_ ®jm[(n?Xg_ GY(X\Ay0_i{÷\E]pkqm_jml9h\Ay Y(pkl j}]\8q?o fihk_ix nkqm_c\Eykxn?ykqmj] jsl_ix¡Xg_io Y(n?Xgfi_io iAW_"XçGY(X ] l9hk% _ hnkfiqmjmx?_"\Ay£x?jm¢(jmo jmY(y£Y8 S { vE| P:S { F { ^ { &hk_"XZC _ H% { # }V¨`A <hk_"y | U LMs{uJD ' F {
(121) ^# D ^! { <hkjmo],_"\Ayko l9h?\8l Y(yk_\EykxY(ykqm|Y(yk_j}yko l/\Aykfi_Y8 LM:{
(122) jmo j}ykjslj\rl _ix¡jml9hkj}y l9hk_&oqsjmfi_ P?jml jmo jykol9\AykfiG _ DF V {=u?ol9\AXgl _i x {
(123) fiqmY(fi¦-fi|kfiqs_io\;Gl _"X l9hk_v_i[Aj}y?ykj}yk[Y8 l/hk_o qmjsfi_A x6l9hk_o fihk_ix nkqs_£jmo¢ð\8qmjmx
(124) u v?YAl9h¨XZ_io Y(n?Xgfi_fiY(ykol9X \8j}yEl o\Aykx¨x?_"p?_"ykx?_"ykfi_fiY(yko l/X \8j}yAlo \AXZ_&o9\rl jm(o _ix
(125)
(126) <hk_ q}\8l l _"X¯fiY(yko l9X\8j}yAl of"\Ayv_o9\8l jm(o _ixv?_if"\Anko_&Y8
(127) lg Yx?j _"XZ_"yAlXg_"\8oY(yko P _ijml9hk_"Xlg Yx?_"p?_"ykx?_"yElfiY(]p?nkl9\rl jmY(yj}yko l/\Aykfi_io\AXg_j}ykjml j}\8l _ixj}y^l9hk_o9\A] _o qmjmfi _ 6lg|÷p_ ` Y(Xl9hk_i|-\AXg_ jykjml j}\8l_ix¡j}y-lg Y0x?j _"XZ_"yAl o qmjmfi_io Ml=|?p?_" i B#¹fiY(n?Xgo_Au(l/hk_p?\AXgl j}\8qRx?_"p?_"yEº x?_"ykfi_-[(X \Ap?hjykx nkfi_ix vE|lg|÷p_¡`fiY(ykol9X \8j}yEl ojmo \rfi|(fiqmjmfAuv?_if"\Anko _-lg|÷p_¡`,x?_"p?_"ykx?_"ykfi_io áâÛ¹Üá}ã.
(128)
(129)
(130) !" #$ %!& !' " (*)+,)-/.0$$"1)+ (
(131) 2.3/4 j}]pYAo _\,p?\AXgl j}\8qY(XZx?_"XYkyl9hk_ Y(p_"X \8l jmY(yko"u?\8fifiYkXgx?j}yk[l Yl/hk_ijX#\Ap?p?\AXgjml jmY(y-Y(XZx?_"X#jsl/hkjy l9hk_0o qmjmfi_A <hk_]\8j}y0jsx?_"\ Yr ¸jmol9hk_MYAqmqmY8j}yk[ 8d o o9n?],_ l9h?\8l _ h?\;¢A_ \ ¢ð\8qmjmxfi|kfiqsjmfofhk_ix nkqm_ Y8¹p_"XgjmY(x GY(X\ [Ajm¢A_"yykn?],v?_"`X M¯Y8¹p?XgY(fi_ioo Y(Xgo"uA\Eykxl9h?\rl _#\EyAll Y0x?_ix nkfi_c\¢ð\8qmjmx o fihk_ix nkqm_,GY(X&\^o9]\rqsqm_"Xykn?],v?_"X M£Y8 p?XgYkfi_io o Y(Xgo; d \;|Yr v?nkjsqmx?j}yk[l9hk_yk_i$ofhk_ix nkqm_ jmo l Y¦8_i_"p-l9hk_0o9\A],_oqsjmfi_,o l9Xnkfil9n?Xg_AukjGí_A lY ¦r_i_"pl9hk_o9\E],_Y(p?_"X\8l jmY(yj}yko l/\Aykfi_io&#jsl/hkjy \©[Ajm¢A_"yKo qmjmfi_A B#fiY(n?Xgo _£ _],jm[(hElyk_i_ix l Y j}ykf"Xg_"\ro _¡l9hk_£o qmjmfi_Oqm_"yk[Al9hKl YOfiY(p_jml9h l9hk_Xg_ix nkfiljsYkyY8 Xg_io Ykn?Xgfi_io" xÍy£YAl/hk_"X Y(Xgx?o;u _ah?\;¢A_,l Y-o l9XZ_il fh l9hk_Xg_ifil9\Ayk[Eqs_,Y8o0j i_ yM l Y v?nkjmqmx¨\Xg_ifil/\Ayk[Aqm_,Y8o 3j i_ M
(132) #o j}yk[l9hkjmojmx?_"\?ulg|÷p_x?_"p_"ykx?_"ykfi_ioa#jsqmq o ljsqmq v?_o9\rl jm(o _ixOj» _,fihkY(YEo _ Qq}\AXg[E_a_"ykYknk[(h= Bykqm|lg|÷p_¡`,x?_"p?_"ykx?_"ykfi_ioh?\;¢A_,l Yv?_ l9\E¦8_"yOj}yEl YO\8fifiY(n?yEl0MY(Xl9hk_-jyEl _"X y?\rqXZ_iY(Xg[(\Ayk3j "\8ljsYkyOY8l9hk_-o qmjmfi_ 6o_i_®jm[(n?Xg_" i nkl o j}ykfi_0l9hk_&fiYkX Xg_io9pY(ykx?j}yk[p?\AXgl j}\8qRx?_"p?_"ykx?_"ykfi_,[(X \Ep?hjmo\8fi|kfiqsjmfAuR _&\AXg_v?XgY(nk[(hElv?\8fi¦,l Y \o l9\Aykx \AXZx \rfi|(fiqmjmf&ofhk_ix nkqmj}yk[p?XgY(vkqm_"] GY(X&hkjmfih]\AyE|l9hk_iYkXg_il jmf"\8qwXZ_io9nkqml o\AXg_&¦kykY8&y xçyp?\AXZl jmf"nkq\EXiu(\o j}]pkqm_&qmjmo l o fihk_ix nkqsj}yk[l_ifh?ykj?nk_cp?XgY8¢kjmx?_io \
(133) hk_"n?Xgjmo l jmf \Aykx l9hk_0o9hkY(Xgl_"Xl/hk_qsYkyk[A_io lp?\8l9h-j}yl9hk_[kX \Ap?hu?l9hk_] Y(Xg_\8fif"n?X \rl _l9hk_hk_"n?Xgjmo l jmfv?Ykn?ykx i. op (k) 1. p1. op1(k+1). time. op2(k). op4(k-1). p2 p3. op3(k). op4(k). op2(k+1). op3(k+1). op6(k). op5(k). op6(k+1). op5(k+1). p4 processors (a). p2. op4(k-1). op5(k). op2(k). op3(k). op4(k) op6(k). op2(k+1) op (k+1) 5. op3(k+1). op1(k+1). p1. op (k) 1. time. op6(k+1). processors. ® jm[(n?Xg_asP-< Y,x?j
(134) _"Xg_"yElc\8qmqmYkf"\8l jmY(yko Y8¯\ o qmjsfi_0Y8[(X \Ap?h)3M F unMyF)" Bykfi_l9hkjmo]\8j}yp?Xgj}ykfij}pkqs_^o _il l qm_ix
(135) uRl9hk_"Xg_Xg_"]\rjy o _i¢A_"X \rqwYkp?_"y ?nk_io l jmY(yko/P `A %Y8)lYafihkYkYAo _l9hk_0jykjml j}\8qo fihk_ix nkqmjyk[ (b). Ü
(136) Ü ×! ü.
(137) `H. . ".$.3 " =
(138) " .
(139) .
(140) 2 . ? %Y8¨l YfihkYkYAo _ l9hk_&Xg_/G_"Xg_"ykfi_oqsjmfi_ <#hk_"Xg_jmo ykYXg_"\ro Y(y *)+ $" l YfhkYkYAo _\ o qmjmfi_ v?_i[Aj}y?ykj}yk[¡\8l&\ fiqsYkfi¦-fi|(fiqm_fiYkyk[(X nk_"yEll YyH,],Ykx nkq}nko ? %Y8 l Yx?_ifijmx?_0l9h?\8l&\Ay^_ix?[A_0jso#Y8 lg|?p?_`Au?hk_"ykfi_0l Yv?_fiYkyko jmx?_"Xg_ix¡j}yl/hk_\8fi|(fiqmjmf p?XgY(vkqm_"] <hk_io_al/h?Xg_i_ ?nk_io l jmY(yko\AXZ_Y8fiY(n?Xgo _0qmjy?¦r_ixOl YA[A_il/hk_"Xi xÍyEl9nkjml jm¢A_iqm|Au
(141) jml o _i_"],o j}]p?Y(XZl9\AyEl l Y 6l9Xg|lY ],j}ykj] 0j i_-v?YAl9h l9hk_qm_"yk[Al9h Y8wl9hk_#qsYkyk[A_io lp?\8l9h jy l9hk_&\8fi|kfiqmjsf [(X \Ep?hu8&hkjmfh,o/hkY(nkqmx v_&\8oo9]\rqsq \ro p?YAoo j}vkqs_,\8o jmljmol jm[(hEl qm|qmj}y?¦8_ix¡lYal/hk_[(n?\AX \AyEl _i_ixv?Y(n?ykx-GY(Xl9hk_qmjmo lo fihk_ix nkqmj}yk[ u \Aykxl9hk_ykn?],v?_"X Y8_ix?[A_ioj}y l9hk_\8fi|kfiqsjmf0[(X \Ap?huko Y\ro lYXg_ix nkfi_l9hk_x?_"p_"ykx?_"ykfi_ fiY(yko l9X\8j}yAl oMY(Xl9hk_,\8fi|kfiqsjmf0o fhk_ix nkqmj}yk[Qp?XZY(vkqm_"] O_jmqmq[Ajm¢A_\-p?Xg_ifijmo _0MY(X]ankq}\8ljsYkyl Y-l9hk_io _ ÷nk_io ljsYkyko\Aykx[Ajm¢A_a\^o YAq}nkl jmY(y _/GY8º Xg_"h?\Eykx
(142) u _Xg_i¢kjm_i)l9hk_fihkYAjmfi_io Y8 ¸. . .
(143)
(144) * 1 ( !. . 0 ". xçy§l9hkjmoao_ifil jmY(y§ __i{÷pkq}\8j}y°jml9hÍnkqmqx?_il9\8jmqmo,l9hk_ ¸§hk_"n?Xgjmo l jmf ª¬«'=`<hk_]\8j}y§jmx?_"\¡jmo \8o#Y(nkl qmj}yk_ixQj}y l9hk_ap?Xg_i¢kjmY(nko o _ifil jmY(y< hk_0fhkYEjsfi_0Y8 ¸^GY(X l9hk_j}ykjml j}\8qo fhk_ix nkqmj}yk[¡jmo l Y fiY(ykojsx?_"Xl9hk_ Y(pklj]^\8q?fi|(fiqmjmf o fhk_ix nkqmj}yk[0MYkX\Ay,j}yw ykjml _cykn?],v?_"XY8
(145) p?XgYkfi_io o Y(Xgo M F 'u jGí_ARjml9hkY(nkl&XZ_io Y(n?Xgfi_fiY(ykol9X \8j}yEl o".
(146) A
(147) !" ²÷· !â²
(148) Ͷ ` !$
(149) â i²÷· "²?i¶ 88²? .
(150) . . > Ykyko jmx?_"Xl/hk_fi|(fiqmjmfo fihk_ix nkqmjyk[-p?XgY(vkqm_"] F !J#mJcJ[" jml9hkYknkl Xg_io Ykn?Xgfi_fiY(yko l/X \8j}yAlo 3Mm F i _il v?_¡\ykY(y?yk_i[k\8l jm¢A_-jyEl _i[A_"X'¹_wyk_-ÍXgY(] \Ay©_ix?[A_/ºÍ _ijm[(hEl _ix¨[(X \Ap?h F "! J # J[ \roGYAqmqmY8oP 0²÷;6 8²÷ ¶
(151) ©d&x?x£l Y3! \^yk_i)¢A_"Xgl _i{"P ! F ! ( ? · R²÷^¶
(152) §d x?xl Y # \Ey-_ix?[A_ÍXgY(]0l Y\8qmq¹YEl9hk_"X¢A_"Xgl jmfi_io(P # F # r ! i ²: ¶
(153) &²?· R²÷ ¶
(154) _w yk_y[ Ue F H j»3e ,*# #¤\Eykx [ Ue F LM:{ V [ Ue j»\eF LM:{(JLM + ,0#- O_h?\;¢A_l9hk_ GYAqmqsY8j}yk[- _iqsq»º=¦kykY8&y¡Xg_io/nkqsl/P ¯²
(155)
(156) Q C ".3$y$$ "z$/ / " .
(157) nCy n .3%( )-n$ /G'/
(158) . áâÛ¹Üá}ã.
(159)
(160)
(161) !" #$ %!& !' " (*)+,)-/.0$$"1)+ (
(162) 2.3/4. .
(163). 0"¶¶. jmo\¢8\8qmjmxQj}ykjml j}\8l jmY(yjyEl _"Xg¢8\8qGu l/hk_"Xg_jmo\,fi|kfiqmjsf^o fhk_ix nkqm_}| LM:{rJD 6x ¡. l9h?\8lo/\8l jmo( _iol9hk_x?_"p_"ykx?_"ykfi_fiY(yko l/X \8j}yAloP. F S{:^# D. / e F LM:{(JLM+ , # PmS{
(164) ^g LM:{ s [ e +^ S + g` > Y(yko jmx?_"X\©fi|(fiqm_ j}y #YAl _£l9h?\8l jmo\Ofi|kfiqm_OY8.-ul YkY ¸?n?]^],j}yk[ \8qmq j}yk_ ÷n?\8qmjml jm_ioZ` l9h?\8lj}yE¢AYAqm¢A_l9hk_0_ix?[A_ioY8 qm_"\8x?o l YP S{
(165) ^g LM:{ # [ e +^ S + # [ [ gH
(166) > Y(yE¢A_"Xgo _iqm|AuEj¬ ?h?\8o ykY0fi|(fiqm_ Y8¹p?YAo jml jm¢A_ _ijm[(hAl;u8Y(yk_&f"\Ey,x?_wyk_AuEMY(X\rqsqOLM0,0!^u l9hk_qmY(yk[A_io lp?\8l9h Mjy) XZY(]l YyLM
(167) ul9h?\8l _x?_"ykYAl _avE| JLM i . wykjml jmY(yu "JLM o/\8l jmo( _io l9hk_ MYEqsqmY8j}yk[-l9Xgj}\Ayk[(nkq}\AX j}yk_ ?n?\8qmjml=|OP / e F ULMs{uJLM+ %,0#mJ "JLM+ ~ "JLM:{ ^[ e . |x?_. jGí_A. <hkjmocp?XZYð¢E_io. / e F LM:{rJLM+ %,0#mJ "JLM:{ O^ ULMs{ "JLM+ ^ [ e l/h?\8l | LMJD =F JLM O^. D-jso\,¢8\8qmjsxfi|kfiqmjsf,o fihk_ix nkqm_A _"]]\`0h?\8olg Yaj}]pY(Xgl9\EyAlfiYkyko _ ÷nk_"ykfi_io/P. jmo \#¢ð\8qmjmx-jykjml j}\8ljsYkyj}yEl _"Xg¢ð\rq ®j}Xgo l"u;[Ajm¢A_"y\Ay0j}yEl _i[A_"X
(168) u"jmljmo_"\8o |0l Yx?_il _"X ] jyk_#j¬ . \Aykx,j»|E_io"u"lYcv?nkjmqmx \ fiYkX Xg_io9pY(ykx?j}yk[fi|kfiqsjmfofhk_ix nkqm_vA|,\Ap?pkqm|(j}yk[ _iqmq}]\AyEºÍ®RY(Xgxío \8qm[AY(Xgjml9h?] ª
(169) Y() y k <hk_ Y(pkl j}]\8qkj}ykjml j}\8l jmY(y,j}yEl _"Xg¢ð\rq °jmol9hk_o9]^\8qmqs_ioljyEl _i[A_"X 0o9nkfh0l9h?\rl h?\8oykY p?YAojsljs¢E_fi|kfiqs_An <hk_"Xg_/GY(Xg_Au FTHj¬& jmo\8fi|kfiqsjmf\Ayk x F)]\8{ ! " # fi|kfiqm_aYr } YAl9hk_"Xg#jso_A. ! ¶â
(170)
(171) ç¶w M ;²÷'¶
(172) 88²÷ d o,o9\8jmxv_/MYkXg_Au
(173) j}y©l9hk_f"\ro _Y8 MOjmx?_"yEl jmf"\8qp?XgYkfi_io o Y(Xgo;u
(174) l9hk_\8qm[AY(Xgjml9h?] if Y(yko jmo l o,j}y©l9hk_ fiY(yE¢A_"XgojsYky¡Yr l9hk_0x?_"p?_"ykx?_"ykfi_-[(X \Ap?h2 j}yEl Y \Ey¡\8fi|kfiqmjsf^[(X \Ap?h) mj o&Ykvkl9\8j}yk_ixOvA|. . . . . . Ü
(175) Ü ×! ü. .
(176) `". . ".$.3 " =
(177) " .
(178) .
(179) 2 . x?_iqm_il j}yk[¨o Y(] __ix?[A_io^Y8 -d&oj}ykjml j}\8q o fihk_ix nkqsj}yk[ u ¸§l/\A¦8_io,l9hk_Y(pkl j}]\rq ofhk_ix nkqmj}yk[ jml9h£n?ykqmj] jsl_ixXZ_io Y(n?Xgfi_io | LM:{(JD ` F JLM:{O ^# DOi d o&Xg_/G_"Xg_"ykfi_o qmjmfi_Au 0¸-l9\A¦8_io\0o qmjmfi_o l/\AXgl j}yk[\8l\,fiqmY(fi¦^fi|(fiqm_fiYkyk[(X nk_"yEl lY H^],Y(x nkq}nko uAjGí_Ak\o qmjmfi_ ÍXgY(] fiqmY(fi¦,fi|kfiqm _ ) n?p l YfiqmYkf¦,fi|kfiqm_ T^O` V¡`A <hkjmo\A],Y(n?yEl o l Y^x?_ifiY(]p?YEo j}yk[ "JLM { j}yAlY JLM:{ ' F {-^ {&hk_"XgC _ H {`# V¨` xçyOYAl/hk_"X YkXgx?o { F JLM:{ ],Y(x > Y(ykojsx?_"X0\Ay_ix?[Am_ eGF LM:{(JLM+ , #- xÍyl9hk_ Xg_/G_"Xg_"ykfi_ o qmjmfi_AuAl9hk_fiY(]p?nkl9\rl jmY(yj}yko l9\Eykfi_ U LMs{uJ V { %jmo p_"XçMYkX ],_ix
(180) n x6 {u^% U LMs{ +8u l9hk_fiY(]p?nkl9\rl jmY(y j}yko l9\Aykfi_Y8s LM+¯&hkjmfhjsop?_"XçGY(X ],_ix0jml9hkj}yl9hk_ Xg_/G_"Xg_"ykfi_o qmjmfi_ Gy?\A],_iqm| LM + J wV + jmoo l9\AXZl _ix v_/MYkXg_l9hk_ _"ykx¡Y8¹l/hk_fiY(]p?nkl9\8ljsYky LM { J wV { i %_"ykfi_l9hkjmo fiY(]^p?nkl9\8l jmY(y-j}yko l9\Eykfi_ LM+nJ V + jmocykYAl l9hk_0Y(yk_l9h?\8l x?_"p_"ykx?on?p?Y(y-fiY(]^pkqs_iljsYkyY8 LM:{(J V { i' xÍy§YAl/hk_"X Y(XZx?o"u V {^T[ e F V +A' <hk_lg Y£fiY(]p?nkl9\rl jmY(yko,jy x?_"p_"ykx?_"ykfi_l9h?XgY(nk[kh_ix?[A% _ e\AXZ_cykYAl#jykjml j}\8l_ix¡j}yl9hk_o/\A],_o qmjmfi_A+ h¯x?[AC _ ef"\Eyv?_o/\;M_iqm| fiY(ykojsx?_"XZ_ix\roc\,lg|?p?W _^_ix?[A_Au?l9hknkof"\Ay£v?_0x?_iqs_il_ix¡ÍXgY(] <hkjmo jmo&l9hk_0\"|^_ix?[A_ioc\EXg_ f"nkl j}y ¸hk_"n?XZjsol jmf ?O_\AXg_qm_ix£l Yl9hk_ GYAqmqmYð#jyk[\8qm[AY(XZjsl/h?] P ! ¶ â
(181) Md&qm[AY(XZjsl/h?] ¸ . "4*)+ }$
(182) %)+$4% ".`
(183) n .3$ C " .3 | " # .3$4G$y (" ( e F ULMs{JLM1+ 2 C " C(
(184) / e '$.$. 2 #"/.0/ ! ("4 # "}.+ % "JL1M + ] Y(x "JLMs { ],Ykx ^g LM:{ #N
(185) )+ ($" C$
(186) % "
(187) n .3$
(188) ( ) 5 pu t "s!$" *$
(189) C " n .3 *
(190) ( ) `
(191) / / $ '"
(192) y2 "}
(193) (()+ (C no "&)-/"/ ")-/ " 4 .0C " .3 | "T$
(194) M )+ ( ! c p(2rt y)F ]\r{
(195) U| "LM:{ Z^ ULMs { 2c%$
(196) %.3 "
(197) }& G$
(198)
(199) " .0 " " # ".$. LM: { ,0# " D ,
(200) | ULMs{uJD F | "LM:{ Z^ J LM:{ ^ sD C .0$m
(201) n .3$ C " .3 <hk_,fiY(XXg_ifil9yk_io oY8 d&qm[AYkXgjml9h?] ¸ f"\Ayv?_,GY(n?ykxj}y¨ª¬«'=OGx lf"\Ay\8qmo Y¡v_ax?_ix nkfi_ix©ÍXgY(] l9hk_0fiY(X Xg_ifil/yk_io oY8d&qm[AYkXgjml9h?]w > Mo _i_¸k_ifil jmY(y ¬?}` ' ÌÉgê9ÉçË ø"Ï6ó;æ¬Õ
(202) æ¬Õ×8Ì9ÏÏ6óðÉöAÉgÕGÏë àÏGÌ î;É=ÏGÉçËÍÙæí×ðÉÏFà/ÊAÉ Égî;ò9ÉgÕgäAÝiÉgÉÝiÉgØgÏ6æ¬Ì ×,û"ä û"ä . . . . . . . . áâÛ¹Üá}ã.
(203)
(204)
(205) !" #$ %!& !' " (*)+,)-/.0$$"1)+ (
(206) 2.3/4 ²?
(207) Ͷw
(208) Or²÷0¶
(209) ! R¶wn}
(210) . . . n5. 0¸[Ajm¢A_io\Ay¡n?p?p_"Xv?Y(n?ykxl Y^l9hk_j}ykjml j}\8l jmY(yj}yEl _"Xg¢8\8q- £Y(vkl9\8j}yk_ixQvE|d qs[EY(Xgjml9h?]¥`A _il v?_l9hk_-Y(pkl j}]\rq Mo9]\8qmqm_io l 0j}ykjml j}\8l jmY(y¨j}yEl _"Xg¢8\8qjml9 h M¨p?XgY(fi_ioo Y(Xgo"' <hk_^GYAqmqsY8j}yk[ j}yk_ ?n?\8qmjslg|£jso _io l9\Evkqsjmo9hk_ix P M M ^ 3 M}V¨` G" &hk_"XZ_ Kjmo l9hk_&qm_"yk[Al/h-Y8
(211) l9hk_&qmY(yk[E_io lp?\8l9h^j y 8EY(Xg_iY8¢A_"Xiu8Y8j}yk[,l Yl/hk_&o l/X \8l _i[A|0GY(X f"nkl ljyk[-_ix?[A_io"u # ^g VK` 6o _i_ _"]^]\`j}yOª»«i i: <hkjmo&j}]pkqmjm_io P M M ^ 3 M%V ` ^ #V¨` &hkjmfihqm_"\8x?o l Y. ` ^ M}V¨` VK` V. M M . . . . ¸ jmol9hk_wXgol[(n?\AX \AyEl _i_ix \8qm[AY(Xgjml9h?] ©_Qo_i_¡ÍXgY(] _ ?n?\8l jmY(y G" ^l9h?\8l-l9hk_Ov?Y(n?ykx 0 x?j}Xg_ifil qm|£x?_"p?_"ykx?on?p?Yky
(212) ukl9hk_qm_"yk[Al9h Y8l9hk_qmY(yk[A_io lp?\8l9h-j}y 8 . . . ?*@
(213)
(214) A !â² O_¡[EY v?\8fi¦§l YOY(n?X,_i{?\A]pkqm_A d o o9n?],_mM F O\;¢ð\8jmq}\Avkqm_Op?XgY(fi_ioo Y(Xgo"¯®j¬º [(n?XZ_ G\ Xg_if"\8qmqmoal/hk_[(X\Ap?h ¤GY(X hkjsfih F `;?xÍy®jm[(n?XZ_ Gv 'u
(215) _x?_"pkjmfil,l9hk_ [(X\Ap?h NuW l9h?\8lap_"X ],jml o,l YfiY(]^p?nkl _ "JLM #MYkX\8qmq\LM 6l9hk_x?j
(216) _"Xg_"yEl¢ð\rqnk_io JLM \AXZ_[Ajm¢A_"y-j}yfij}Xgfiqm_ioY(y-l9hk_ [(n?XZ_ \EykxQ\Ay^Y(pkl j}]\8q%o fhk_ix nkqm_0jml9h¡n?ykqmj}],jml _ixOXg_io Y(n?XZfi_io | LMJD ' F "JLM ^# DO <hkjmo&o fihk_ix nkqm_\8o&\8q}Xg_"\rx?|¡Xg_"p?Xg_io _"yEl _ix®jm[(n?Xg_as P p?XZY8º fi_io oY(Xgo\AXZ_¡yk_i_ix?_ix
(217) ®jm[(n?Xg_ 6f ,o9hkY8o,l9hk_¡\8fi|kfiqmjmfQ[kX \Ap?h -Ykvkl9\8j}yk_ix vA|¨f"nkll j}yk[ _ix?[A_i#o e#F LM { JLM + o/nkfh l9h?\8l + { ^ U LM { hk_"Xg_ { F JLM { ],Y(x 0R®jy?\rqsqm|Au ®jm[(n?Xg_ 6x #o9hkY8o\p?YAoo j}vkqs_^o fhk_ix nkqm_-Y8Y(p_"X \8l jmY(ykop?XgY8¢kjmx?_ix vA|¡\-qmjmo lo fihk_ix nkqmj}yk[ u GY(X &hkjmfih }F)A? . . ! - & . ). _il nko o/n?]]\AXgj3i_d qm[AY(Xgjml9h?] 0¸\roGYAqmqmY8oPwXgo lfiY(]p?nkl _l9hk_ ¢ð\rqnk_io "JLM ¯j}y. . l Y¨p?XgY8¢kjsx?_£l9hk_¡Ykpkl j}]\8q o fhk_ix nkqmj}yk[ #jsl/hkY(nklXg_io Ykn?Xgfi_¡fiY(ykol9X \8j}yEl o | \<#hk_"y¨l9\A¦r_¡\ Xg_/G_"Xg_"ykfi_0o qmjsfi_,o l/\AXgl j}yk[\8l l Ykp H],Y(x P | U LM { JD = F { ^ D#^! { jml9hH% { # V¨` ®j}y?\8qmqm|Au
(218) x?_iqm_il _0ÍXgY(] "4% _ix?[E_iol9h?\8l&yk_ifi_io o/\AXgjmqm|QfiYkX Xg_io9pY(ykx¡l Y-x?_"p?_"ykx?_"ykfi_io,v?_ilgº _i_"yx?j
(219) _"Xg_"yElo qmjmfi_io P .+ l/hkYAo _,_ix?[A_iG o e%F LM:{uJLM+ o9nkfh£l9h?\r l {^ LM:{ +a\EXg_ Xg_"] Yð¢E_ix¡vA| ¸ Ü
(220) Ü ×! ü.
(221) `. ".$.3 " =
(222) " . . 4 op2. 1 14 op6. 0 0. 0. op3 2. s. 2. 0. 10 op5 0 -23. (a) 0 op1. op4 op2. op3. -6. 0. op3. 0 0. 2. 4. 4. -10. op12 4. op2 6. 0 op1. op6 10 10. -10 op5 0. 10 (b). op5. op6 0. (c) p. 1. 25. op4. op1. 1 op1 1.
(223) 2 . 6 op4. 1 2.
(224) . op5. p2. processors. op2. time. op6 op3. ®jm[(n?Xg_ P G\" P:<hk_XZ_ix nkfi_ix¡x?_"p?_"ykx?_"ykfi_^[(X \Ap?h)mP F `" Gv P:<hk_0[(X \Ap?) h NUW 6f P:<hk_,\8fi|(fiqmjmf[kX \Ap?) h 6x Pkd fiY(X Xg_io9pY(ykx?j}yk[qmjsol&o fihk_ix nkqmj}yk[¡\8qmqsYkf"\8l jmY(yOP }F)A (d). . áâÛ¹Üá}ã.
(225) .
(226)
(227) !" #$ %!& !' " (*)+,)-/.0$$"1)+ (
(228) 2.3/4. %Y8 _i¢A_"Xiu;_ix?[A_iol9h?\8lfiY(X XZ_io9p?Y(ykx,l Y x?_"p?_"ykx?_"ykfi_io v?_ilg _i_"yx?j
(229) _"Xg_"yElo qmjmfi_io\EXg_l9hkYEo _ o9nkfih0l9h?\8l {F +n^%[ Ue ixÍykx?_i_ix
(230) u8#jsl/hkjy l9hk_Xg_/G_"Xg_"ykfi_ o qmjsfi_Au8l/hk_o fihk_ix nkqm_ixfiY(]p?nkl9\rl jmY(y j}yko l9\Eykfi_ioa\AXg_ LM:{(J V! { \Aykx LM+nJ V! + MY(X#_ix?[A_}e%F LM:{(JLM+ '<hk_"Xg_/GY(Xg_AuRl9hk_ fiY(]^p?nkl9\8l jmY(y LM+nJ V {"^v[ U e iuE&hkjmfh-x?_"p_"ykx?o&n?p?Yky LM:{J V { iukjmo&p_"XçMYkX ],_ix-jy l9hk_#o9\A],_ o qmjmfi_&j V {^y[ e F IV +ku8jGí_A +^m[ e ' F {g" B l9hk_"Xgjmo _AuEjsljmo p?_"X=MY(X],_ix j}y§\o9n?vko _ ?nk_"yElo qmjmfi_Au\AykxOj}yOl/hkjso,f"\8o_ +^ [ e {g= <hk_"XZ_/MY(XZ_Aul9hk_fiY(ykx?jml jmY(y©GY(X f"nkl ljyk[_ix?[A_io,fiY(XXg_io9p?Ykykx?jyk[l Y£x?_"p?_"ykx?_"ykfi_iov?_ilg _i_"yOx?j
(231) _"Xg_"yEl,o qmjsfi_io 6jGí_A
(232) l9hkYEo _ _ f"\8qmqm_ixlg|÷p_,x?_"p?_"ykx?_"ykfi_io &Xgjml _io + ^[ e { X \8l9hk_"X l/h?\Ay { ^ LM { + _ilcnko#fhk_ifi¦-l9hkjmoc]^\8l9hk_"]\8ljsf"\rqsqm|AO > Y(yko jmx?_"X \,¢ð\rqsjmxfi|kfiqsjmf,o fihk_ix nkqmjykz [ | LM:{uJD ' F S{O^ D\Aykxqm_iGl S{ F {^ {#jsl/hOykY8 } { ^ yV `Au&hk_"Xg_ jmo,[Ajm¢A_"Oy P _ qmYkY(¦¡\8l\Ay£\AX vkjml9X \AXZ|o qmjsfi_^Y8 qm_"yk[Al/h
(233) ?® Y(X#_"\8fih_ix?[A} _ e#F LM { JLM + iuRl9hk_x?_"p_"ykx?_"ykfi_ fiY(ykol9X \8j}yEljmo&o9\rl jm(o _ix
(234) u?l9hknko {:^ LM:{ ^ {= + ^ + ^[ e i: <hk_"yu {:^ U LMs{ O ^# {` +'^# +'^[ e {V + ^ LM:{ * # +'^[ U e' V { V 1^ #` # +'^g[ e` V { V` + ^[ e ' V { H} + ^[ e = V { ®wn?Xgl9hk_"X],Y(Xg_Au;j» + ^y[ e
(235) V {+FIH?u"l/hk_"yl/hk_x?_"p?_"ykx?_"ykfi_ fiY(yko l9X\8j}yAl ox?j}Xg_ifilqs|,&XZjsl_io { ^ U LMs{ +8- >Y(yA¢E_"Xgo _iqm|Aukj¬ {"^ LM:{ +8ukl9hk_"y-yk_ifi_io o9\AXgjmqm| +=^[ e V {gHsPAj» \Ay _ix?[A_jmof"nklvA| 0¸u?l9hk_"y jsljmo\8qmo Y-f"nklcvE|Y(n?Xyk_i X nkqm_ARO_a\EXg_qm_ixl Y\] Y(x?j _ix ¢A_"XZo jmY(y-Y8 0¸&hkjmfih _ f"\8qmq] ¸?¸kj}ykfi_ _&f"nkl ],Y(Xg_ _ix?[A_ioj}y] 0¸l9h?\Ey-jy 0¸ukl9hk_ \8fi|kfiqmjmf[(X\Ap? h ) Y(vkl/\8j}yk_ix vA|] ¸fiY(yAl/\8j}yko\o9n?vko _ilYr l9hk__ix?[E_ioY8 l9hk_\8fi|(fiqmjmf [(X\Ap?) h 8 ¸k_i_0®jm[(n?Xg_,l Y^jsqmq}nko l9X\8l _l/hkjso#Í\8fil" . . 0. op2. op3. 24 time. op4. op6 (a). op5. p1 p2. op5 op4. op1. op1. op3. op2. op6. processors. ®jm[(n?Xg_sP G\" P:<hk_\rfi|(fiqmjmf,[(X \Ap?hp?XgY8¢kjmx?_ixQvE|d qm[AY(Xgjml9h?]¤] ¸ Gv Pkd fiY(X Xg_io9pY(ykx?j}yk[qmjsol&o fihk_ix nkqmj}yk[¡\8qmqsYkf"\8l jmY(Oy P }F) (b). _c\EXg_cykY8 Xg_"\8x?|l YMYkX ],nkq\rl _&l/hk_cp?XgYkvkqs_"] (©_cyk_i_ix¡yk_ijml9hk_"X\Ey,j}ykjslj\rq¹Y(XZx?_"Xgj}yk[ O ykY(X\¨XZ_/M_"Xg_"ykfi_©o qmjsfi_§\AyA|KqmY(yk[A_"Xi )h?\8l- _QYkykqs| yk_i_ix)jmo¡l Y§x?_il _"X ] jyk_§\© n?ykfil jmY(y Ü
(236) Ü ×! ü.
(237) `"«. . %P!EV°o9nkfh-l/h?\8lP. / e F ZJ , #yJ +^ [ Ue `V. ".$.3 " =
(238) " .
(239) .
(240) 2 . ~gH. ¸?nkfih\#Ín?ykfil jmY(y jmof"\8qmqm_ix \ ($4% j}y,l9hk_ fiY(yEl _i{klY8wo |?ykfih?XgY(ykY(nko '
(241) ¸:xfij}Xgf"nkjml o&ª»;= _ilj] jyk[£jmo\Ay¡\8oo jm[(y?],_"yElY8 \Ayj}yEl _i[A_"X q}\8[ #l Y_"\8fih£¢A_"Xgl _i{ , !mPRjml\A],Y(n?yEl o l Y£o9n?p?p?Xg_io o 9XZ_i[Ajmo l _"Xgo lYl9hk_ _ijm[(hAlYr_"\rfh_ix?[E_qm_"\"¢kj}yk[ 6&hkYAo_l9\8jmqjmo \Aykx-l Y\8x?x Xg_i[Ejsol _"XgolY_"\8fh _ix?[A__"yEl _"Xgj}yk[ 6&hkYEo _&hk_"\8xjmo i"x lqm_"\8x?o l Y\0yk_i _ix?[A_/ºÍ _ijm[(hEl j}yk[Ín?ykfil jmY( y [ x?_ wyk_ixGY(X \Ay-_ix?[A _ vE| [ U e' FT[ e ^! Z V i d#Ml_"X\-o9nkjml9\Avkqm_ XZ_il j}],j}yk[¡jmoGY(n?ykx
(242) u _,x?_ wyk_l9hk_\8fi|kfiqmjmf[(X\Ap?h ) ,\8o GYAqmqsY8/o P
(243) \Ay _ix?[Am _ e , #¤jmo¦8_"pklj}y ) 0j jml o,yk_i _ijm[(hEC l [ U e jmG o H 6_ix?[A_ #jsl/hkY(nklXg_i[Ajmo l _"X i > qm_"\AXZqs|Au ) jmo\8fi|kfiqmjsf G\8o o9n?] _l9hk_"Xg_0jmo\fi|kfiqm_Au
(244) \Aykxo9n?] n?pXg_ilj] _ixQ_ix?[E_ _ijm[(hAlo Y(y l9hkjmofi|kfiqs_ l Y[A_il\ fiYkyAl9X\8x?jmfil jmY(y i jm¢A_"y ) 8u8 _ qmjmo l o fhk_ix nkqm_ jml \8o\ d &hkYEo _ ¢A_"XZl jmfi_ioc\AXZ_ _ijm[(hEl _ix¡vE|l/hk_j}ykjml j}\8q Ín?ykfil jmY(y _if"\8qmq¹l/h?\8l Y(n?X [AY(\rqw\8o#l Y\Ayko _"X l9hk_lg Y0MYAqmqmY8j}yk[ ?nk_io l jmY(yko/P h hkYAo _qmY(yk[A_io lp?\8l9hh?\ro %Y8)lYaf"nkl _ix?[A_iooY\8ol Y^Y(vkl9\8j}y\Ay\8fi|kfiqmjmfa[kX \Ap?) ],j}ykj}]\8qqs_"yk[El9h %Y8 l Y¨f"nkl\8o¡]\AyE| _ix?[E_ioQ\8o¡pYAo o j}vkqm_ oY l9h?\8ll/hk_ykn?],v?_"X Y8ax?_"p_"ykx?_"ykfi_ fiY(yko l9X\8j}yAl o#l Yv?_o/\8l jm(o _ixQvE|-l9hk_qmjsolgºÍo fihk_ix nkqsj}y[¡Y8 jmoc],j}ykj}],3j i_ix Y8unko j}yk[¡Y(n?Xyk_i MYkX ],nkq\rl jmY(yu _,f"\Ayol9\8l _0Y(n?X Y(vk~g_ifil jm¢A_io],Y(XZ_ p?XZ_ifijso_iqs|©jy l _"X],oY8Xg_il j}],j}yk[ P i²?8 ² ®jykx \ XZ_il j}],j}yk[ l/h?\8l],j}ykj}],3j i_io¡l9hk_qmY(yk[E_io l p?\rl9h¨j}y ) 8ujGí_Ajy l _"X ],oYr%XZ_il j}],j}yk[ uAl9h?\rl ],j}ykj}],3j i_iol9hk_fiqmYkf¦^p?_"XgjmYkx °Y8wl9hk_Xg_il j}],_ix^[(X \Ap?h Mo _i_ ¸k_ifil jmY(y i i²?8 ² ®jykx\XZ_il j}],j}yk[ o Yl/h?\8ll9hk_y(n?],v?_"X¯Y8
(245) _ix?[A_io j}y ) jmo] jykj}]\rqMujM _A x?jmo l9Xgj}v?nkl _,Xg_i[Ajmo l _"Xgo o Y\8olYqm_"\"¢E_\8o G_i)_ix?[A_iojml9hkYknklcXg_i[Ejsol _"Xgo&\8opYAo o j}vkqm_A xÍy¨¸k_ifil jmY(y u _o9hkY8¤hkYðl YO\8fihkjs_i¢E_l9hk_ wXgo l,Y(v÷~=_ifil jm¢A_ 6l9hkjmo,jmo\¡ _iqmq»º=¦(ykY8&y p?XgYkvkqs_"] i' <hk_"Xg_¡\AXg_-o _i¢A_"X\8q pYAo o j}vkqm_¡o YEqnkljsYkyko"u\Aykx j}y¨¸k_ifil jmY(y¨u¹ _o/hkYð¤hkY8+l Y o _iqm_ifil£l9hk_Ov?_io lY(yk_jml9h Xg_io/p?_ifill Y§l9hk_o _ifiY(ykx Y(vk~g_ifil jm¢A_Au \Aykx _Qol9\8l _£Y(n?% X wy?\rq \8qm[AYkXgjml9h?]?O_j}]p?XZYð¢E_n?p?Y(y ¸^GY(X lg YaXg_"\8oY(yko P wXgol _h?\;¢A_\v_il l _"XvY(n?ykx
(246) u\Aykx o _ifiYkykx¡ _f"nkl&],Y(XZ__ix?[A_io"u hk_"ykfi_,],Y(Xg_ ÍXg_i_ix?Y(]GY(X l/hk_qsjmo l o fihk_ix nkqmjyk[R . . . . . . . . . . . . . áâÛ¹Üá}ã.
(247)
(248)
(249) !" #$ %!& !' " (*)+,)-/.0$$"1)+ (
(250) 2.3/4 . //2 /
(251) .! R$*,
(252) ! % .
(253) *^ . <hk_"XZ_\AXg_, _iqmq¬º=¦kykY8&y§Xg_il j}],j}yk[Q\8qm[AYkXgjml9h?],ol9h?\8lf"\EyOv?_nko_ixOl Y¡],j}ykj}],j3i_l9hk_,fiqmY(fi¦ p_"XgjmY(xKY8c\ ' %¸:x fij}Xgf"nkjml" Íx y§l9hkjmoo _ifiljsYkyu¹ _-o9hkY8¤hkYð+l YOnko _o/nkfh§\8qm[AY(Xgjml9h?] ol Y x?_"Xgjm¢A_,\,¢ð\rqsjmx¢ð\rqnk_ LM:{ MY(X_"\8fih-Y(p_"X \8l Y(X*LMs={ . . ( . ®RY(X ]\8qmqm|Au \OXg_il j}],j}yk[§Y8\[(X \Ap?h RF !J#mJ/Jc[ jmo\¢A_"Xgl_i{AºÍq}\Av_iqsj}yk[§Ín?ykfil jmY(y P ! V 0 §p?_"XçGY(X ],o\§l9X \EykogMYkX ]\8l jmY(y§Yrl9hk_jykjml j}\8q0[(X \Ap?h j}yAlY \ yk_i [(X\Ap?h _ [ jso x?_ wyk_ixO\8oMYEqsqmY8o Pj¬\ e F ZJ jmo\Ay-_ix?[A_Yr #l9hk_"y F " !J$#mJcJ[ hk_"XgC [ e' FI[ e ^! = V e ¸?nkfih \XZ_il j}],j}yk[¡jmo,¢ð\8qmjmx j» GY(X _"\8fih_ix?[Ay _ e,Yr #-Ou [ e ~ H?YEl _,l9h?\8l _\8o o/n?],_ix l9h?\rlj}y\EyA|0fi|(fiqm_ Y8 $l9hk_"XZ_jmo \8lqs_"\ro lY(yk_#_ix?[A_&hkYAo_ _ijs[khAljso p?YAojsljs¢E"_ P÷nkojyk [ '
(254) :¸ x l _"X],j}ykYAqmYA[A|AuR _o/\" | jmo&o|÷ykfih?XgY(ykY(nko; _ijmo _"Xgo Y(y§\Aykx¨¸?\8{k_¡ª¬'p?Xg_io_"yAl0o _i¢A_"X \8q\rqs[EY(Xgjml9h?],o,l YfiY(]^p?nkl _\Ay )+$4% ". ¢ð\8qmjmx Xg_ilj] jyk[Ru(j}y-l9hk_ o _"yko _ l9h?\8ll9hk_qmY(yk[A_iolp?\rl9hYr%yknkqmq _ijm[(hElj}y-l9hk_Xg_il j}],_ix-[(X \Ep?h,jmo\ro o9hkYkXgl \ro¹p?YAoo j}vkqs_A _/MY(XZ_ p?Xg_io _"yEl j}yk[ l9hk_io _ \rqs[EY(Xgjml9h?],ojml9h,],Y(Xg_x?_il/\8jmqso;u8 _yk_i_ix,o Yk],_ x?_ wykjml jmY(yko"%O_,x?_"ykYAl _vE| ¡\-p?\8l9 h Y8 +ÍXgY( ] lY RuwvEq | [ F
Documents relatifs
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des
2) Le développement local c'est-à-dire les expériences d'intervention en développement économique communautaire, en économie sociale et en économie solidaire mises
La définition générale du concept d'évaluation formative des apprentissages retenue pour cette recherche constitue une synthèse découlant de la recension d'un ensemble
Effets et pouvoirs de la voix dans la philosophie et la littérature antiques Paris, Classiques Garnier, 2021 (Kaïnon - Anthropologie de la pensée ancienne, 19), ISBN :
relève de traités, et que les États membres sont des États au sens du droit international public, c’est à ce juste titre que J. Fischer peut qualifier l’Union actuelle de
Afin de saisir le déploiement de ce discours, j'analyserai dans un premier temps les représentations liées au temps dans le roman, en m'arrêtant d'abord sur toutes celles qui,
Cette recherche, de type qualitatif, consiste en une exploration de la littérature dont les buts sont de décrire selon divers auteurs, différe ntes expériences
For each sam- pling point is also given the value output of the merging process with the difference between the SH degree 100 expansions subtracted, the index corresponding to the
