A new aproach to parallel sparse cholesky factorization on distributed memory parallel computers

(1)

HAL Id: inria-00074590

https://hal.inria.fr/inria-00074590

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.

A new aproach to parallel sparse cholesky factorization on distributed memory parallel computers

Mounir Hahad, Jocelyne Erhel, Thierry Priol

To cite this version:

Mounir Hahad, Jocelyne Erhel, Thierry Priol. A new aproach to parallel sparse cholesky factorization on distributed memory parallel computers. [Research Report] RR-2081, INRIA. 1993. �inria-00074590�

(2)

ISSN 0249-6399

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

a p p o r t

d e r e c h e r c h e

1 9 9 3

PROGRAMME 1

Architectures parallèles, bases de données, réseaux et systèmes distribués

A New Approach

to Parallel Sparse Cholesky Factorization on Distributed Memory Parallel Computers

Mounir HAHAD, Jocelyne ERHEL, Thierry PRIOL

N˚ 2081

Octobre 1993

(3)

(4)

! "#$%'&$(*)

+ -,.

,0/

$/21,

-,354

%687 9:+ '(; <$9:=4

>@?BA'C'DFEGIH#G#H#JLKMNO?QPSRUTWVXC'RZY\[G#Y]%M_^+`'DFRUEEaVcb[edafI]

gihkjmlShonqpprstvuwhoxzy|{~}krax}k|hzr%Bnhn~r~rUOnkrUrUjS|rraOh|rzrnU

r}zz}rperU{~k}zhk{~|r

g'hzjr}%gOugOu

nq|Ojmhk}Urhzrxzy|rhxkyrUmS|stvx}kjmhkr#smSwtsaOnlmr

$¡¢£¤¥B¦q£m§©¨jª«nS|naU'|hzjmlmhnpep{~|lI¬{z}khz{|}kr®prpejmhk¯Bnhn~~rxjmpe||}zrhk

°±

g²-³'r´Sjmµmr}ky|r$¶z|j%Bn{~Qq|j%ln{~|·%{¸Urn¹QºyOn}'{~q»Wjmhnwlm{~´mr|hzjm|~rp¼}zjOr

kjS´Sr%{~+Bnhn~~r½}zy|rprkonqlmrOnkz{~|l%|hkjSlmhonqppe{l_pej¬¬rm{~U´mjS´Sr¬{z}khz{|}k{~|l

}ky|r|nq}on$nqB$}zy|rxjSp||}n}z{jS|npjS|l%}ky|r\|hkj|xrzkjShk¹-¾Ly{~rw}ky|{~xnqBr%rnqk{~~

»Wrnqk{~|~r-»Wjmhª_r~Ok}zhkBx}z|hkrahkjmrpq{}xnq$Brxjmpr-»½n{~hk~+yBnh+jm$||z}khzBx}khkr

jm|r¿~{~µmr+kBnqhkzr$pIn}zhk{ÀÁxjmpe||}n}k{~jS|¹%Â½Ã}zy|{~OnOrhXª_r$xjS|k{¸Urh+nhzr¸n}z{´Sr~

|rªÄnq||hkjUnmxzy}zj{~p|~rperU}k{~|l}zy|r_²-y|jS~rkµUw»nmx}kjmhz{~Ån}z{jS%jmn

±

¯g²5hk||{~|ln

kyBnqhkr0´U{hz}kBnq|prpjmhz

°ÆUÇ

³¹Sºy|rnq|k}zhonSx}k{~jm$jq»n%kyOnhkra$prpjmhz%jm$}kjS$j»n

U{~k}zhk{~||}zrperpjShk%n~~jªQ|}zj%{U}zhkj|UBxrnw¸nhzlmrÈ½lmhn{~%»nSx}kjShk{~Ånq}k{~jm$n~lmjShk{~}kypÁ

kUBxzy|hzjm|{~År¯ª{~}kyr´mrU}ka¹

Æ

r´mrhn'oxzy|raU|~{~|l#k}khn}zrlm{~rnhzrxjSpBnqhkr¿¿nqBerUÈ

Brhk{~prU}zxjSBUBx}zrÃzje»nhwky|jªÉ}kyBnq}}zy|{~n||hzjnSxkyÃxnqÃ|hkj´U{¸Ur}zy|r$Bjª-rh%j»

±

g²-nO$}kyrrnzrj»'|hkjSlmhnppe{~|lª{~}ky#zyBnhzr#´mnhz{¸n|~ra¹

ÊeËÌ¿ÍzÎÏO¤mÐ¢q§ÒÑwu%¨

Æ

yBnqhkr

Ç

{~hk}zBn#rpjmhz²-y|jS~rkµU»nSx}kjShk{~Ånq}k{~jmQ-}nkµ

oxzy|r¬|~{lBUkOnhkzrpInq}khz{Óxr¹

Ô¸Õ$Ö

×Ø½ÙÚ

Ö

×'Û'Ü~Ø½ÝÞß

àká½â~ãäåçæèémäémäêmëìåçíFåïîWäqðñïí

Unit´e de recherche INRIA Rennes

IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France) Téléphone : (33) 99 84 71 00 – Télécopie : (33) 99 38 38 32

(5)

m

-,'

,0/:6! "I0%&0(:6 9:

-,%¼ 4#%

4I % 9:¯,/I%¼ +\9 \9 $, 65,

-,354 %

Ë|¢ Ë@§ r||~jm{~}onq}k{~jmÃrIxnmxrÁ¬rIp#nmxzy|{~|r+Bnqhon~½r~rn5pLrpejm{~hkr$U{~k}zhk{ÀÈ

|rr¯«rxrzk{~}krÃUrer¿jmhk}z#{peBjShk}nU}k¬r¸n5Bnhz}Ur}k{~~{n}zr|hka¹'r¿r}a_¸n

p{~kr%r%|´Uhkrçnq||~{¸xn}z{jS|Bnqhon~½r~r%|n|%~rpej¬¿r~rUr+|hkjSlmhonqpp#n}k{ÀjmeBnh

rU´mjS{_UrperknlSrhkrm{rhk}$||r#U{~k}zhk{~||}z{jS=¬rUjm«rr$n{~|z{S|rUrxnq¸x|~

k|h~rU{rhkrU}z|hzj¬xrkzr|hka¹Q²-r}z}kr%}! nSxkyrOr|}zr%h|r´-r~rh%xjmpe|~r|rkhUr|hzjÈ

|rpr{~hkh|rlm|~{~rhk-}kr"S|r~rxn¸x|Ok|hp#n}zhk{¸xr_xhkr|zr¹

±

n_xr}nqhk}k{¸x~rmS|jS|

xjmk{¸-rhzjm|%||r\|jm|´Sr~~rn|hkj|xzy|rUr+¸n\»nmx}zjmhz{n}z{jSUr²-yjm~rkµUUrp#n}zhk{¸xr

xhkr|kr$z|h~rp#nmxzy|{~|rn#pLrpjS{~hkrU{~k}zhk{~|rr#Ujm}|rr$||r$pLrpjS{hzr´U{~hk}kr~r

Bnhz}onqlrrm¹#$çnk}khnmx}z{~jmI%|r%pLrpejm{~hkrBnqhk}nlrr nqUrkz|%|r%pLrpejm{~hkr|yUSÈ

k{&S|rU{~k}zhk{~|rr|jm|Brhzpr}-{U}zhkj|U|{~hkr-|nqlSjmhz{}zy|pr-Ur-»nmx}kjmhz{~on}z{~jmnlShonq{

¸nhklSrkUBxzy|hzjm|{~|rBnqhr´-r|rprU}ka¹Qg'~|z{r|hkz}khn}|rlm{~r$jmho¬jm|BnqBxrperU}zjmU}

xjmpeBnh|rra¹'¿rh|rz|~}on}z_nmx}k|r~pejmU}khzrU}$mr|jm|'Ojm|´Sjm|-nOjm|}z{hnw||r}k{~~{ïÈ

onq}k{~jm$rIxnmxrUrp#nmxzy|{~|rBnhn~r~rn\pLrpejm{~hkr_¬{z}khz{«rrm}kjm}_r#xjmkrhz´mnU}

(na´mnqU}onlSr||r+|hkjSlmhonqpp#n}k{Àjm#n{~|rr$lSh! nSxrÁneÓnexjmpep$||{¸xnq}k{~jmeBnh%´mnhz{¸n|~r

Bnhz}onqlrra¹

)@ÏB£¢Ío¦+*,Ë@§ Ñu¨-@rpejm{~hkr

Ç

{~hz}k|r~~rg'nhk}nlrrm'»½nmx}zjmhk{~n}k{~jS®¬rÁ²-y|jm~rzµU

jmhUjm|OnBxrprU}Up#n}zhk{¸xrxhkr|kra¹

(6)

; < /

654#

,$/

Â½%pInUxjSp|}on}z{~jmBnqµSrhk|raa}ky|rzjm~|}z{jS%}kjn-kOnhkzr_~{~|rnqh¿kUk}zrp {~¿hzr S|{~hkr¿¹

ºy|{~_zUk}krp p#nanhz{zr%{e´mnhz{jS||hzjm|~rpeSkBxzyn-}kyr ¬{xhkr}k{~Ån}z{~jm#j»'Bnhz}k{¸n

U{ rhkrU}k{¸nq|r SBn}z{~jm|arBxjS|U}krhzr0»Wjmh'{~|z}onOxr{~$xjmpe||}onq}k{~jmOn=B|{¸+UUBnpe{Óx

jmhek}khzBx}z|honqnBnq~z{~¹?>w|{~}zrÁjq»W}krX_}zy|r5pIn}zhk{Àcjq»jmhUrhA@@{~zpepr}zhk{¸x#nB

BjSk{~}k{~´SrUrBB|{~}zrm'kj5}kyBnq}n¯U{~hkrx}$per}kyj¬5{~U´mjS~´{~|le}½ª_j5k}zr|xnqÄOr|zr }kj

kjS´Sr}zy|rkUz}krpDCFEGIHKJ

sm¹»nSx}kjShk{~År}kyrpIn}zhk{ÀLCL{~}zy|r-»WjShkpMCNGPOQOKRªy|rhkrFO5{~nw~jª_rh}khk{¸nq|lm|¸nqh

pInq}khz{ï:S

|¹-kjS~´mr%}ky|r%}½ª-j$}khz{Ónq|lmÓnqh_zUk}krp:OQTUGPH%nB8OKRQEVGIT¹

ºy|{~¿BnOrhUrnq¿ª{~}zy}ky|rWBBhkz}Qk}zr+ªy|{¸xky%{~xn~~rw}ky|r_²-yjm~rkµUw»nSx}kjShk{~Ån}z{~jmQ¹

¾Ãrxjm|z{¸Urhn|rªcn|hkjUnmxzy}kj%xjmpe||}z{l_}zy|r_U|perhk{¸xnq»nSx}kjShk{~Ånq}k{~jm%{~Bnqhon~~r

jmÁneU{~k}zhk{~||}zr5prpejmhz$Bnhn~~rxjmpe||}krh

°±

g²³hz|||{~|l#nekyBnqhkr¯´U{hz}kBnq

prpejmhz

°½ÆUÇ

³¹|ºy|r ÆUÇ

{~%n+BnlSrSÈkUrpInqB$zyBnhzr5nm|Uhzrk%zBnmxr+||{~~}-jmÁn

|yUUk{¸xn~~U{~k}zhk{~||}zrperpjShkU¹¾Ãr_Or~{~r´mr-}kyOn}'{~}{~n+{~U}krhzrk}z{ln~}krhkBnq}k{~´mr-}kj

xjmU´SrU}k{~jmBnq

±

g²-QhkjmlShonqpp{À|l_nq||hkjUnmxzy|ra¹au

ÆUÇ

n~~jªB|X}kj{~prprU}

n¸nqhklmrÈlShon{~#n~lmjShk{~}ky|p¼jSZn

±

g²%UhkrUOx{~|l|hzj|xrkzjmh%{~U}krhnmx}z{jS|¹UÂ½OUrr¿¿n

¸nhklSrlShon{~#}onqkµe{#}zy|r²-y|jSrkµU$»nSx}kjShk{~Ånq}k{~jm#hkrm{hzrzr´mrhonxjS~|pnSxxrzkra

ªy|{¸xzypIna$Or%|jm#~j|xnQnSxxrzkra¹QÂ½n+U{~k}zhk{~||}zr#rU´U{~hkjmprU}Uªyrhkrxjm~|p

nhzrpInq|Or$jS}zj~j|xnq¿prpejmhk{~ramn\|hkj|xrzkjShxnq||jm}hzrnmXªhk{~}zr n}on\k}zjmhzr#jm

jm}zy|rh'|hkj|xrkkjShka¹Uºy{~}xn|jm}nmxzy|{~r´Sr_{~}z}nzµª{~}kyjm|}X}ky|r{~h_xjmU}khz{|}k{~jmX¹¾Ãr

xjmOx~BUr}zyBn}|j$¸nqhklmr\lmhonq{~I²-y|jSrkµUe»nmx}zjmhz{Åan}k{~jS{~Ojmzk{~|~r%jmÁxjSU´mrU}k{~jSBn

~j¬xnperpjShk#p$|~}k{~|hzj¬xrkzjmhka¹ZYr|r(BB}k{~|l5»Whzjmp}kyr ÆUÇ

ÃQª-ryOna´mrI¬rk{~lmrÄn

¸nhklSr$lmhn{~cnqlSjmhz{}zy|p©zUBxzy|hkjS|{~Årª{~}kyÃr´mrU}ka¹X|Orhk{~perU}k+ª_rhzrxjmB¬Bx}kra

jm#n+kj»F}½ª«nqhkr%Bnzr

ÆUÇ

Bxnq~reÑu¨¹

ºy|r¸namjS|}'j»Q}zy|{~_BnqBrh_{~_nq»WjS~jª[Jm{~$zrx}k{~jSZª-r{~U}khkj|UOxr}zy|r%kr S|r¬È

}k{¸n²-yjm~rkµU »nmx}zjmhz{Åan}k{~jSQ¹'Â½Lkrax}k{~jm@|'r|{~k}z{lÃBnhn~~rnqlSjmhz{}zy|pa¿pInq{~|~

}ky|rU\BnqUÈÂ½nqBe}ky|r]\On¬È w|}aBnhzr|hz{r(=B#j´mrhz´{~rª-r¿¹Â½krax}k{~jm_^B|ª-r{~U}khzj¬¬Bxr

jm|h$n|hkjUnmxzyLxjm|z{~k}k{~|l5j»%}ky|rÑwu¨ kyBnqhkr ´U{~hk}zBnperpjShkUB}zy|r#U|prhz{¸xn

»nmx}kjmhz{~Ån}z{jSÁn~lSjmhk{~}zy|p nqB#}zy|r$oxzy|r¬|~{lIz}khn}krlm{~r¹ìÂ½Ázrx}k{~jS`|Oª_r+|hzj´{¸Ur

r|Brhk{~prU}nOhkrz|~}k»Fjmhne{~}zr¿Âkg

Æ

² XS+hk||{~|lÑwu%¨

ÆUÇ

ÃS»Wj|x|z{ljSI}zy|r

ÆUÇ

OryBna´U{~jmha¹

a

\ '! "I$%'&$(*)

+ -,.

,0/

ºy|r~r»W}wyBnOz{Ó¬rj»QBOlm|hzrIs\ky|jª%nUrkr²-y|jSrkµUe»nmx}zjmhz{Åan}k{~jSÁn~lmjShk{~}kypÁ¹

²-jm|zrx|}z{~´mrxjSp|%j»:O nhzrxjmpe||}zrUOrh »Wjmhzp{~|lnekrhz{rjq»«|¿|nq}kr+}kj

rnmxzy#xjm~|peQ¹m¨jS}kr%}kyOn}-{ï»'}ky|r%r~rperU}?Ocb2d%{~ÅrhkjOUªy|{¸xzy{~_jq»W}krI}zy|rxnkr\{ï»Q}zy|r

pInq}khk{À${~kBnqhkkrSB}zy|r~jUjm $eUjUrw|jm}w{~´Sjm~´mr%xjmpe||}n}k{~jS|¹SÂ½#jm}kyrhª-jmhU{ï»

(7)

è ! "$#%

& è'!)( #%

*%+ -,

è ! ."/#%

0213 0413)(50

176

K 0 386

9):;#<=

9-:#<=

0>3?3 A@ 0>3B3

*CDE, è GF !."/#%

0413 0213IHJ0%3B3

9-:#<=

è ! "5#%

&K5LM=NJOPBMRQS0%3

àUTVW YX#%

*%+ -,ZKL;M=NJOPBMRQ[0

à3 T

#%

0213 0413)(50

176

K 0 386

9):;#<=

9-:#<=

0>3?3 \@ 0>3B3

*CDE,]K5LM=NJOPBMRQS0>3

àUT

#>

0413 0213IHJ0%3B3

9-:#<=

\X{~lm|hzrsJ|²-jm~|peUÈ ²-yjm~rkµU\»Wjmh¬r|kr\pIn}zhk{¸xrnO$»FjmhkOnhkzrjmr¹

nmxxjm|U}}zy|{~Onhk}z{¸x|¸nhOjm{~U}'~rnmU}kjnwkBnqhkkr%²-y|jm~rzµU»nSx}kjShk{~Ånq}k{~jm$n~lmjShk{~}kypÁ¹

ºy|r#hk{~lmyU}eyBnB z{Ó¬rj» BBlS|hkrÄs#zy|jªzBxzyn@n~lmjShk{~}ky|pªy|rhkrA^2_U`aZbc_

° O bed ³

{~}zy|rzr}jq»xjm~|pek|oxhz{}k+j»|jmÃÅrhkj5r~rprU}z{~Ã}zy|rUggfBh#hkjª¼j»:O'nB

^G_U`a]bc_

°

Odbm³{-}kyrzr}j»QhzjªLk|oxhz{~|}kwj»Q|jSÅrhzj$r~rpr}z_{~$}zy|r ggf?h$xjm~|pX¹

ikj

lmmmmn e o

p o

orq o

s o

t o o

ouowvxo

o o oxyro

o o{z

|J}

}}}

~ j lmmmmn e p owq

s t

oxouv

o o ouy

oorz

|J}

}}}

~

3 6

2 1 4 5

7 8

\X{~lmhkr!J

Æ

Onhkzr%pIn}zhk{À$k}khzBx}z|hkrnqB${~}k²-yjm~rkµU0»nmx}zjmhnqBer~{pe{~Bn}z{j+}khzrr

±

hk{~|lÃ}kyr#»nmx}kjmhz{~Ån}z{jS|hkj|xrzn BOÀÈ½{~Ä|y|r|jmper|jmj|xxhk$JkjSpr#Århzj

r~rpr}z{~ C OrxjSpr+|jm5Århzj{~6O¹ \X{~lmhkr$zy|jªneonpe|~rpInq}khz{ïnB¯{~}k

²-y|jm~rzµU$»nSx}kjSh

°

n5¶U·{~AO pInq}oxzy|rn-BB~¸³¹UÂ½#jShoUrhw}kj$na´mrxjSp|}on}z{~jm|nB

k}zjmhonqlmrmS{~}{~_ª-jmhz}kyUªy|{~~r}kjhzrUBxr}kyBnq}$BB~ÀÈ{~Qqªy|{¸xky#UrOrBUjS$}ky|rwjmhUrhk{~|l+j»

(8)

{~}ky|hzrr-k}kr|QJUsÈ¿jmho¬rhk{~|l:S È zp$Ojm~{¸xì»nmx}kjmhz{~Ån}z{jSFS È U|perhk{¸xnq»nSx}kjShk{~Ån}z{~jmQ¹

whoUrhz{~|lmnqhkrBnqkrejSIyr|hk{~z}k{¸x}zj$hkr¬Bxr}zy|r BB~ÀÈ{~nqB0»Wjmhzjmprwj»'}ky|rp5U}kj

r|yBnqBxr}zy|rBnqhonq~r~{~kp5¹¿ÂF»|jm}an5BjSk}ÈjShoUrhz{~|lÄ}zrxzy||{&S|r}kyOn}$r|yOnBxrI}zy|r

Bnhn~~r~{~kp ª{~}zyIner S|{~´mn~rU} BB~ïÈ½{~$pInaOrUrz{hn|~rw»WjSh_Bnqhonq~r»nSx}kjShk{~Ån}z{~jmQ¹

Æ

Up$BjS~{Óx»½nmx}zjmhk{~Ånq}k{~jm#zr}kw|kjSpr|nq}on+k}zhkBx}k|hzrnOrk}k{~p#n}kr}ky|rnqpjS|U}

j»k}zjmhonqlmr$hzr S|{~hkr¿¹'w|r$j»}zy|rzrI|nq}onek}zhkBx}z|hkr${\}ky|r$r~{~p{~Bnq}k{~jm#}zhkrrej»:O¹

¿{~~si¬roxhz{~Br%}zy|rhzjm~r%j»}ky{wk}zhkBx}z|hkr${~#Ojm}ky#zr S|rU}k{¸nnqB#Bnqhon~~rO»nSxzÈ

}kjShk{~Ån}z{~jmQ¹ \X{~Bnq~U|}zy|rU|perhk{¸xnq'»nmx}kjmhz{~Ån}z{jSÁOrh »Wjmhzp}zy|rr´mnq~Bn}z{jSj»}zy|r

r~rpr}zj»ZO¹

Æ

{~Bxr}zy|{~_¸nqk}|yOnkrw{~_}zy|rpejmk}}k{~prxjmk|pe{lBª-r»Wj|x_jS{~}k

Bnhn~~r~{~Ån}z{jSQ¹

% ¯,w +\= +I%

¾ÃrUj$jm}nmUhkrz»WhzjmU}onqQnBep$|~}z{ï»FhkjmU}n|per}ky|j|Uç||Q{#}zy|{~BnOrh¹ºy|rzr

jmhz{lS{~Bn~~n{~prÃnq}hkj´U{¸U{~|lÁn \kjm~|}z{~jmÃ}kj5yU|lmrekBnqhkzrkUk}zrpa¹

ºy|r$nhzrBnqkrejmn k||p#n}zhk{Ànzkrp$$n}rnmxzyz}kr#jq»Q}ky|r»nmx}zjmhz{Åan}k{~jSnB$n

pjShkrrIx{~rU}-{~||rh-~jjSªy|{¸xzyIna´Sjm{¸U{~B¬{hzrx}z{jS|¹S¾Ãrnqhkr%{~U}krhzrk}zre{e~rkzjÈ

|y|{~k}z{¸xn}zr¬{hzrx}'pr}ky|j|Ua¹ ²-jS|krmrU}k~aª-r_ª{~~mrp|yBnqk{~År-}ky|r-}½ª-jª-r~µU|jª

\BnqUÈ½Â½nBV\OnUÈkw|}n||hzjnSxkyr

e

nO+}ky|r{~h{~prp$rU}on}z{~jmjS$BjS}kyzyBnhzreprÈ

pjShknB+U{~k}zhk{~||}zr+prpjmhz%Bnhn~~r|xjmpe||}krhk¹qºy|r}½ª_j\pjmz}Qhzr~r´mnU}Ojm{~U}k

{~}kyrkrnq~lmjmhz{~}ky|pe_nhzr}zy|r}nkµeBnhz}k{~}k{~jS|{~|lnO}zy|r%oxzy|r¬|~{lB¹

"!#!#$

Â½%~sSs& ¿{~hzr´U{~rªkjSprxjmpe||}n}k{~jSBnSpj|Ur~alSr|rhn~~ª_rk|{~}kra+}kjxjm~|pe

jmhz{r}zr¯»nSx}kjShk{~Ån}z{~jm|a¹¿¾Ãr$|hk{~r=O=Uroxhz{Or#}ky|r$perU{~|p lShon{~ÄnqB5¸nhklSrlShonq{

}onqkµpej¬¬r~¹ºyr BB|r-lmhonq{~pj|UrU{~'j»B~rz{~U}krhzrk}amz{Oxr{~}Q{~X»Whk|{~}zrk'}kj%r||~jm{~}

kBxzyn+Bnqhon~~r~{~kp¼jm

±

g²-a¹

u©»½n{~hk~Äz{~p|~r#ª«na}zjclSr|rhn}zrÃprU{~|p lmhn{~L}nkµU{~e}kjlmhzjm|nq~}zy|r

jmOrhonq}k{~jmª{}zy|{~InqI{~|rh~jjS{~U}kj$n+k{~|lSrw}onqkµ¿¹|ºª-jzBxzy}onqkµUxn#Br%|{~}

{~}kyr ²-yjm~rkµU0»nmx}zjmhz{Åan}k{~jS$»Whzjmp<}zy|r~jUjm|" e nqB p J

'

#"(V*),+.-Y)/QJU|¿|n}zrxjSpUgUIxjm~|p f °

f10 ^G_U`aZbc_

°

Ocb d³z³¿

'

#2)043+5- /QJUoxnq~r xjm~|p gU}zy|r% SBnhzrhkjUjS}j»{~}zU{¸nlmjSBnOr~rperU}¹

\|hzjmpÉ}ky|{~Sn%|hkraxrUrOxrhkrÓnq}k{~jm+lmhn|yxn$Or||{~~}'jm$}zy|rBnz{~j»Q}zy|r-»Wjm~~jª{~|l

UrOrBUrBxÁxjS|k}zhonq{U}z J

'

#"(V*),+.-Y)/xn|jm}Or%r|rx|}zrOr»WjShkrA#2)&0637+3)&/

'

#2)043+5- /xn|jm}Orr¬rax|}kraOr»WjShkrnq #"(V*),+.-Y)/Lf10 ^G_U`a]bU_

°O b d ³¹

+

(9)

8

x y x

Cdiv(x) Cmod(x,y)

8 6 8 5

6 5 8 7

7

7 3 7 1 7 6

1

3 6

4 6 2

3

2 4 5

\X{~lm|hzr!JUºnzµ$|hkrxrUrBxr$lmhonq|ye»Wjmh-pInq}khz{ï$j»$BBlS|hkr

¨jm}zr}zyBn}»WjmhwrnmxzyÃxjm~|peg}ky|rhzr${~nxjmhkhzrkOjmOU{~|lP#2)043+5- /}onqkµ¿¿nBI»Wjmh

rnmxzy+j+OÈ ¬{ÓnqlmjSBnS|jm+Århzjr~rpr}QOcb2dU}kyrhkr{~n%xjmhzhkrzBjSBU{~|lA#"(V*),+5-J)&/_}onqkµ¿¹

rOxrm}zy|r#}onqkµÄhkrxraUrBxrÃlShonq|ycUr|{¸x}kr®{ BBlmhkr5yBn

°

O³+´mrhz}k{¸xr#nB

° °

O³@¿³-rUlSrªy|rhkr

°

O³{~-}ky|r\p$Brh-j»'|jmÅrhkjer~rpr}z{~ O¹

Â½Ãjmho¬rh}zjjm}on{~ÃnxjUnhkzrh+}onzµÁlShonq{X¿}ky|repr¬{p lmhonq{~Á}nkµU #2)063+nB

#"(;)nqhkrBnSxzµmr\}kjSlmr}zy|rh{~zBxzynªnan'}kjwk{~p{À»Ww}ky|r-|hzrxrUrBxr%lmhn|y$nB

}kj#p{~|{~p${~År%kUBxzy|hzjm|{~Ånq}k{~jmX¹Qºª-j#hkr~r´mnq}%¸nhzlmr$lShon{~5}onqkµpej¬¬r~yOna´mr+Brr

{~}zhkj|UBxr0»WjmhzyBnhzr#prpjmhzpInSxzy|{~|r

°

khk´mrmr#U ¿{~{~ ~sSsW³[J

'

{~#}ky|rL\OnUÈ½Â½Inq||hkjUnmxzyQOnz{lm~r%}onzµ{~UrBO|r#U:J

b G[#"(;)

°

g f|³!f 0 ^G_U`aZbc_

°

Ocb d³ #2)&063

°

gq³cS

'

{~#}ky|rL\OnUÈkw|}n~lmjShk{~}kypÁmn\k{~|lSr%}nkµe{~«Ur(BB|r#U J

d G #2)&063

°

f³#"(V*)

°

g f|³g 0 ^G_U`aZbc_

°O d d ³

Æ

{~Bxrn~¿k|}onqkµU%j»in+z{~|lm~r%}onqkµ b jmh d nqhkr%oxzy|raU|~r¯{ekr S|rBxrm¿}zy|rhzr

{~|j+|rr0}kj+µmrre}ky|r%|hzrxr¬rBxr+hkr¸nq}k{~jm$Or}½ª-rr#}ky|rp<{~$}ky|r%}onqkµ$|hzrxr¬rBxr

lmhn|yQ¹K\||hz}ky|rhkpjShkrmìª_r$|jS}kre}kyBnq}kjSpr+|hkrxrUrBxrhkr¸nq}k{~jm|\Br}½ª-rr ´mrhz}k{¸xr

nhzrhkr¬|B|nq}%nBZpIna$OrU{~oxnqhoUra}zjjO¹|ºy|{~lShonyhkr¬Bx}k{~jS~rnmUw}kj#n+}khkrr

ªy|{¸xzyÄ{~$prhzr~Ã}ky|r#r~{~p{~Bnq}k{~jm5}khzrrjq»}kyrIp#n}zhk{À=}zjÃBre»nSx}kjShkrì¹Â½}${~rank

}kj5´mrhz{À»WÁ}zyBn} byOn

°

Ocbeda³\prU{~|plShon{~Ãz||}onqkµUInqB d#yBn

°

Oddm³\kBxzy

k|}onzµU¹rxn~}zyBn}

°

O.beda³${~}zy|rU|p$Orh$j»|jS|ÅrhzjcrrprU}k${~Lhzjª gÃj»

O nB

°

Oddm³\{\}ky|rep$Brh\j»|jS|ÅrhzjÁr~rperU}k{~ÄxjS~|p f¿¹'#jmhzrj´mrhaQ}zy|r

(10)

2 1 4 5 7

8

T( j ) J( k )

3 6 4

6 4 7 1

7 3 7 6

7

8 7 8 6 8 5

8

6 5 5 6

2 3 2

4

6 4 6 5

5

3 1 6

7 3 7 1 7 6 7

8 7 8 6

8

5

3 1 3 2

2

8

redundant

\X{~lmhkr ^JUºnzµ|hzrxr¬rBxr$lShonyZnqB$r{~pe{On}k{~jS}zhkrrm¹

(11)

&! $

w

±

g²-aQxjSp|%nhkr$z|hkranmÃnpejm|l$}zy|r$|hzj¬xrkzjmhk+|hz{jSh%}kjnUÁxjSp|}onaÈ

}k{~jmX¹mºy|rw}onqkµ$oxzy|raU|~{~|ljSU´{~jS|k~$UrOrBUwjm}zy|{~_{~|{~}z{ÓnqBxjSp+pIn|{~|lB¹Â½

BjS}kye}ky|rU{~k}zhk{~||}zr8\BnqUÈ½Â½ ~s&nBe}zy|rU{~k}khz{~||}kra \On¬È w|}`n~lmjShk{~}ky|pe}zy|r

pr¬{p<lmhn{~}onqkµpej|UrQ{~%|zrª{~}zy=U{¿rhkr}xjS~|pnzk{~lmprU}z}khn}krlm{~r¹

Y+xjmU}khnz}S}ky|rhzr{~|j%zBxzyIxjS|k}zhon{~U}

°

xjm~|pepInq||{~|l³O}zjoxzy|raU|~r}zy|r}onqkµU

jm#n+kyBnqhkr#perpjShkp#nmxzy|{~|r%nB0kjBOn¸nqhklmr%lShon{~epj|UrQxnq#Br%|zr¿¹

\|jShU{~k}zhk{~||}zrÃperpjShkp#nmxzy|{~|ra¿}kyrVBBhzk}+r|Brhz{~prU}k+jmÃ}zy|r \On¬ÈÂ½ÄnqïÈ

lmjShk{~}ky|p s&%ª_rhkrÁxnqhkhz{raÄjS|}$jmp#n}khz{¸xrnhz{~k{~|l¯»WhkjSp |{~|rÈOjm{~U}LBO|{~}krÁU{¿rÈ

hkrOxr%jmOrhonq}kjmhz_jS$hkrx}onlm|¸nh-lmhz{¸U¹Sºy|rrk}zr#U{~kkrax}k{~jm#jShoUrhz{~|l QnB+}zy|r

k|}khkrrÈ}zjÈ½k|¿x|Or5pIn|{~|lnhzrIkr¿-nmxzy|{~r´U{~|l~jª BB~ÀÈ½{ÄnqBÃlSjUj¬ ~jnS

Bn¸nqBxr-»WjSh}ky|rw|hkjS|~rp|BUrhxjS|k{¸Urhn}z{jSQ¹SºyS}ky|rwBrh»WjmhzpInqBxr-jm|}n{~|r

nhzrBr}z}krh-}kyOn+»WjSh}zy|rU{~k}zhk{~||}zr \On¬Èw|}n~lSjmhk{~}zy|pÁ¹Â½BUrrìm}zy|r¸n}k}zrh{~|zr

}kjzjm~´mrUBO|{~}krrrprU}k\|hkjS|~rpnqhk{~k{~|lZ»WhkjSp OÈ½kyOnOr }khk{¸nq|lm|¸nqhperkyr¹'u

k{~pr%ªhnUÈknhzjm|BZ}onzµÁnzk{~lmprU}{~%|kr5na»F}krhn$rk}zrÃU{~kzrx}k{~jSÃjmho¬rhk{~|l

j»'}ky|r%}krk}p#n}zhk{¸xr `k¹

\|jSh$kyBnqhkrperpjShkp#nmxzy|{~|ra%rjShklmr#r}#n½¹^;|zrk}zhonq{lSyU}½»WjShkªnho¬Ã}zy|r

¸nhklSr%lmhonq{~I}nzµIpej|Ur¿{~#}ky|r]\On¬ÈÂ½n~lSjmhk{~}zy|pÁ¹ jª-r´mrh|}zy|rUje|jm}ryBnBxr

}ky|r+Bnqhon~~r~{~kp UÁneOjmk}\jmho¬rhk{~|l#j»}kyr$r~{pe{~Bn}z{jS}zhkrrm¹XÂ½Ãn S|{~}zrU{ rhzrU}

ª«naU¿jS}kyUBrhkl#r}$n½¹s _}onqµmrnSU´mnU}onqlmr+j»n#¸nhzlmrh%}onqkµ5lmhn{~Áz{~År?JQnZ}onzµÁ{~

}ky|r%xjmpe|~r}k{~jSjq»n%kr}jq»xjmU}z{lS|jm«xjS~|p|'{~$}kyr ²-yjm~rkµU\»nmx}kjmh-}kyOn}-kyBnqhkr

rkzrU}k{¸n~~%}ky|r-onqprzBnhzk{~}½%k}zhkBx}z|hkrS¹ jª-r´mrhaa{}X}k|hz|'jm|}'}zyBn}X}ky|rzrkjxnq~r

k|Orhz|j|Urnhzrj»W}zr}zjj$¸nqhklmr%}zjn~~jªn+lmjUj|ejUnmeBnqÓnqBx{~|lO¹Uºy|rhkr»WjmhzrmO}ky|r

nhzrk|~{~}nmxxjmho¬{l}kj#nek{~p|~r%y|rhk{~k}z{Óx\{~U}khkj|UOxr¯{ s2`k¹ jm}zyOrhzlr}nq½¹BUj

|jm}X|krnwUUBnpe{¸xQ~jUnm%Bnq¸nBx{~|l}zrxzy||{&S|rr´Sr}zy|jmlmy+}ky|r-pInSxky{r}ky|rr|BrÈ

hk{~pr}ª{}zy#yBnn\kyBnqhkrZprpejmhkU¹k{~|l+|#}kj$r{~lmyU}|hzj|xrkzjmhzO}ky|{~nqlSjmhz{}zy|p

r|y|{~|{~}k-Br}k}krhOrh»WjmhzpInOxr}kyOn#}ky|rL\OnUÈ½Â½e»Wjmh-kyOnhkra#prpejmhzpInSxky{r¹

7

¾L{~}ky#}kyrnmU´SrU}j»-kyBnqhkr¯´U{hz}kBnq'prpejmhk$p#nmxzy|{~|r

°

~{~µmrÑwrO|n~

Æ

SBnhzrrÈ

krnqhoxzyÑ

Æ

sa³Un%|rª@|hkjSlmhnppe{ï|lwBnhnmU{~lSp {~_hkj´U{¸Ur JUxjmpe||}krhk-ª{}zy|yUSÈ

k{¸xnq~ÄU{~z}khk{~|}krperpjShkÁxnLOr|hzjmlmhnpepr¯|k{~|lÄn5zyBnhzr ´mnhk{¸nq|~r|hzjÈ

lmhnpp${~|lwpj|Ur½¹Uw´U{~jmk~S}kyrlSjnqB{~}kj+UUBnz}ky|r%¸nmxzµ$j»'|hkjSlmhnppe{~|lr¬È

´U{hzjm|perU}k»Wjmh

±

g²-Oªy|{¸xzypInqµmr-{~}U{Ix|~}}kj#nmxzy|{~r´mr\y|{~lmy#Brh½»WjShkpInqBxra¹

¾Ãr_}nµSr«nSU´mnU}onqlmr-j»¿}ky|{~'|rªLxjSBxr}_}zjhkrzrU}«nqn~lmjShk{~}ky|p@}kyOn}|zrn¸nqhklmr

lmhn{~}nkµepj|UrO|Ojmn+U{~k}khz{~||}kra#prpejmhznhxky{}zrx}z|hkrm¿nqBe}kyBnq}r|khkr%{~}k

kUBxzy|hzjm|{~Ånq}k{~jmeeprnq|-j»r´mrU}ka¹

! #" #$%&' ")(

*$$ Á{~n

ÆUÇ

"{~pe|~rp$rU}kr jm$n+Â½}zr 0 #,+.--yUUBrhx|Orç;k¹aÂ½}'{~rp$BrUr

(12)

Link

Proc. 2 Proc. 3

Proc. 0 Proc. 1

local memory local memory local memory local memory

Link

Proc. 3

Proc. 1 Proc. 0

Proc. 2 Virtual address space Page

Virtual address space

Proc. 1

Proc. 2 Proc. 0

Proc. 3

Traditional view Koan SVM New user’s view

Mapping

\X{~lmhkrL`!Jºy|r

Æ

yBnhzr

Ç

{~hk}zBn'#rpejmhk$nk}khnmx}z{~jm

|j|Ura¹'nmxzy+|j|Ur-{Ox~BUrn80

° s #yÅ³mnq|lmperU}kr nq 0 K=BjUn}z{l

BjS{~}%|hzj|xrkzjmh

°

Smeµ=Bjm|\Brnqµ|³QnqB ^#U}zrjq»«p#n{~prpjmhzBnqhk}z{}z{~jm|r

{~}zj$BnlSr%j»Q^S YU}krranmxzyQ¹Oºy|rzr|j|Ur nqhkr+{~}zrhoxjm||rax}kr5{~Án0yUOrhx|Or

}kjSBjSjSlmU¹¿ºy|r#p{~|{~p+|p }k{~per}kj5krBn5kpInq~przonqlmrOr}½ª-rrL}½ª-j5|j|Ur{~

|¹çpe¹º'j+krOnperknlSrjq»jS|r%BnlSrz{~ÅrmB¹çpe«nqhkr%|rxrkonqhkU¹

*$Z<|hkj´U{¸Ure}ky|r¯|krh#ª{~}kyLn5´U{~hk}zBn%nm|Uhzrk#zBnmxrS_zyBnhzr Lnq}zy|r

|hkj|xrkkjShka¹Â½}${~Onhk}z{~}k{~jm|ra5{U}zjÁBnqlmr+j»%r SBnz{~År

°

^S UU}krn¿jmhUr U

}ky|r# w³+ªy|{¸xkynhzrIz|hkranmnpejm|l#}kyrIhkj|xrzkjmhz -~j|xn-prpejmhz{r¹ \|hk}zy|rh È

pjShkrmU}zy|rkyOnhkrazBnmxr+xnOrz|~{}w{~}zjn+kr}%jq»ihzrlm{~jS|jq»nqhk|{~}zhonhzz{ÅrmOrnmxzy

j»_}zy|rppInqBnlSreª{~}kyÃnI¬{¿rhzrU}xjSy|rhzrBxre|hkjS}kj|xjm~s^;k¹Oºy|r|nq}onek}zjmhkra5{

n#hkranm!Xqªhk{~}kr#pj|Ur

°

}ky|r#zBnhzkr#pInq}khk{ÀB³w{~p#nBnqlmr5ª{~}kyÄn¯k}zhkjS|l=xjmy|rhzrBxUJ

kr´Srhonq:,)xjS|{~r%j»«n0BnlSrp#naxjUr|{z}%jmÃU{ rhzrU}%|hkj|xrzkjShkX||}%}zy|rÁnqhkr

{~´mnq~{Ón}kran'zjjSnqnLQ0OjSBrhon}z{~jm+j¬xx|hka¹

Æ

UBxzy|hzjm|{~Ånq}k{~jm+prxzyBnq|{~kpe nqhkr

|hkj´U{¸Ur\}kj\pInOnlmr-p$|}zBnUrBx~|z{jSQ¹ * Z {-n~kj%k||~{~r+ª{~}ky$Orh½»WjShkp#nBxr

prnqk|hzrpr}-}kjUjS

°

n~Qz}onq}k{~k}z{ÓxnO#}k{~p{~|lS_nOjm}n#r|rx|}k{~jmO³¿nB#n0}khonSxr

lmrrhonq}kjmh-»½nmx{~~{~}½¹

" , ! ' " "!#

ÂkUrnq~U|jS|rª-jmÓZ|kr$nekyBnqhkr¯´U{hz}kBnq'prpejmhkepInSxky{ri|k}%~{~µmrne|yUUk{¸xnq~

kyBnqhkr5perpjShkepInmxzy|{~|rS¹B¾Ãr${~pe|~rp$rU}krZ}ky|r$z|Brhk|j||nq:\BnqUÈ w|}nqlSjmhz{}zy|p

k||~{ra#ª{~}ky}zy|r

Æ

g$¿u

Æ

ÉBrOxkypInhzµ ~sk|ªy{Óxzy5{~ªhk{~}z}kr¯»Wjmh%n$zyBnhzr5prÈ

pjShk5Bnhn~~rxjmpe||}zrh%çk¹ jª-r´Srhhkrz|~}kjq»}zy|{~$r|Brhz{~prU}$kyjª }zyBn}n

kyBnqhkr ´U{hz}kBnqprpjmhz#pInmxzy|{~|r+kyjm|¸5|jS}Bre|kraÄn$n#hzrn-kyBnqhkr prpejmhz

pInSxky{rm¹mºyrp#n{~$|hzjm|~rpe_rOxjm|U}zrhkr¯ª{~}kye}ky|{~n~lSjmhk{~}zy|p<nhkr J

(13)

'

oxzy|raU|~{~|l:J¿nUUBnqp{¸xw}onqkµ#oxzy|r¬|~{lBO|k{~|l#n$}nkµ S|rr{~}zy|rzyBnhzr

nmUhkrzzBnmxrSB{~|jS}_r Ix{~rU}U|r%}zj$p$|~}k{~|~rnmxxrk%xjm =O{Óx}k$S

'

xhz{}z{¸xnXkrx}z{~jm|$JU}ky|{~n~lmjShk{~}kyp hzr S|{~hkr

°

O³ @xjS~|p$~j|xzµ{~|lS«nqB#n

pInqU}onqkµS|r|rw~j¬xzµU{~|lm-n-}ky|rhzrnhkrwk|Orhz|j|Ur{~$}zy|rp#n}khz{ÀO8Sm}zy|{~_{~

}kjUj$p$BxzyejmIn+p#nmxzy|{~|rjSIªy{Óxzy#~j|xkµUnqhkr%|jm}r Ix{~rU}k~{~prp$rU}kr S

'

nnw|hkj|xrkkjShr|rx|}zrn }onzµ d q{}pIna%ªhk{~}krw}kjnq~pjmz}nq}ky|rwhk{~lmyU}'Bnhz}

j»+}ky|rp#n}zhk{À

°

BnqlmrxjSU}on{~|{~|lÄxjm~|p${ ^G_U`aZbc_

°O dd ³k³#xnk{~|lÄOnlmr

{~U´mn~{¸|n}z{jS|_nqB$y|{~lSyZn}on\}khnIx¹

Ix{~rU}UUBnpe{¸x~jnS$BnqÓnqBx{~|l+ª{~}ky~jª@j´mrhzy|rnSjS

±

¯g²-krrpyOnho

}kjnSxzy|{~r´mrm¹Uºyrhkr»FjmhkrSUª_rwjm|}»Wjmh-nz}on}z{¸x}onqkµnqkk{~lS|prU}jS$}ky|rwBnz{~_jq»n~r´Sr

U|p$Brhk{~|l$j»-}ky|r+r~{~p{~Bn}z{~jm$}khzrrm¿zj#}kyBnq}ª-rz|||hzrk+}ky|r$nmxxrk+xjmU}khzjm}zjIn

}onqkµ S|r|rm¹ìÂ½ÁjShoUrh%}zjIpe{~|{~p${ÅrBnqlmr$xjm =O{Óx}knB¯}kjek||hkrzxjm~|p#~j|xzµa

~r»W}½È½~jUjmµU{~|lpr}zy|j|Unhzrp$BxzypjShkr{~U}krhzrk}z{~|lB¹Urxn~|}kyOn}'ª_rkrnw¸nhklSr_lShonq{

}onqkµ$pj|Ur¹ rBxrm¿n$xjSp${~_pej|U{BBr$U$jS|~$jm|r%|hzj¬xrkzjmh¹Oºy|r\hkrp#n{~|{~|l

BnlSrxjm =B{¸x}znqhkr#U|r$}kjZ»n~kr+kyOnhk{~|lOQz{~Bxr$BnS|U{~|l{~%|jm}\hkrnq{~z}k{¸x+ª{~}kyÃ}kjUj

¸nhklSrn+Bnqlmr%k{~ÅrS¹

! ! ! &$" " ) '

uz}onq}kr0rnhz{~rhamjS|h_nqlSjmhz{}zy|p {~k}zhonq{lSyU}½»WjShkªnho¬+Urhk{~´Sr+»WhzjmpÉ}ky|rwkr S|rU}z{Ónq

~r»W}%~jjSµU{ln~lmjShk{~}ky|p5¹|Â½}xnqÄn~kj#Or$krrÄnqn8\BnqUÈ½Â½=nqlSjmhz{}zy|p"k{~Bxr#n~'|UÈ

|n}zr%}kjnxjm~|pnqhkr+ln}zy|rhzr5{~}zjIn0k{~|lm~r5¶onq}kjmpe{¸x·}nzµ ¹ìu~Q}zy|rkre|¿|n}zr

nhzr«xjSp|}kr%U%jmr_|hzj|xrkzjmh-ªy|rhzrn{~}zy|rU{~k}khz{~||}kraV\BnqUÈÂ½\}ky|r+nhkrU{~k}zhk{ÀÈ

||}zr$jSkr´mrhnQhkj|xrzkjmhz¹O¾Ly|rIn\}onzµUg{~_xjSp|~r}zr¿U}kyrxjSpUg{~_hzrnmU

}kjepj|U{À»WxjSp|w{\^2_U`aZbc_

°O db ³¹

Æ

{~Bxr

° f gq³%nhzrr¬rax|}kra5jmÃU{ rhzrU}

|hkj|xrkkjShk¬rBrBU{~|l#jm}zy|r+oxzy|rU{~|lej»_}zy|r+}onzµU d }ky|rkr$|hzj¬xrkzjmhk+p$|z}

Br+{~U»WjShkpra}zyBn}%}zy|r$}onqkµ b {~%xjmpe|~r}krì¹Bºyrhkrnqhkr$kr´mrhnzjm~|}k{~jS|%}kj#}ky|{~

kUBxzy|hzjm|{~Ånq}k{~jmÃ|hzjm|~rp5¿{~Bx~BU{~|l¯kyBnqhkrnhzhonaU$nB5r´SrU}ka¹Â½ÄjS|hjS|{~|{~jmQ

r´mr}z_~rnS+}kjOr}z}krhOrh½»Fjmhkp#nBxrmmz{~Bxr}zy|rxnqOrrnqk{~~nO$rIx{~rU}z+yBnqBSÈ

~r$n}}zy|rzUk}krp<µmrhz|rO~r´mrOUpernj»¿przonqlmra¹mºª-j%»W|Ox}k{~jmxn~~Bnqpr~

nO!

"#$

Qn~~jª Ojmz}k{~|lÃnÄr´mrU}$nB ª«nq{}z{~|le»Wjmh$nÃr´SrU}$}kj

Brek{~lmOn~r¿¹XÂ½ÄjS|h${~p|~rp$rU}n}k{~jSQ

%&

k}+|hkjUnm|xnqk}znperknlmre}kj

n~-|hkj|xrzkjShkInqB!

"#$

{~n5|~j|xzµU{l#»W|Bx}k{~jmxn~½¹nmxzy|hkj|xrzkjShpInq{~UÈ

}onq{_n~j|xnq xjSU$j»inq~|r´mr}z}kyBnq}_j|xx|hkhzrU|hz{~|l}zy|r%r|rx|}z{~jmInqB$jr´SrU}

¹¿¨jS}kr+}kyBnq}%}ky|{~n~lmjShk{~}kyp UjUr%|jS}%}onµSrnSU´mnU}nlmr\j»«nq#zBrx{Ónqoxzy|raU|~{~|l

}krxzy|{S|rQJ}ky|r\jm|}zrh~jjS{~k{~pe|~U{~z}khk{~|}kr#jS#}ky|rna´mn{~¸nrhkj|xrzkjmhz%{n

x|x~{¸xªnaU¹|rxnq~Q}kyOn}}kyrjm|}z{~pInOoxzy|raU|~{~|ljq»n+}nzµlmhn|y

°

r´SrÁn+}khzrr³wjm

kr´Srhonq|hzj¬xrkzjmhk${~¨gÈxjSp|~r}zrm¹ jª_r´Srhì{}%{~{~U}krhzrk}z{~|l}kj#zrr}zy|r$r¿rx}k

j»«¬{¿rhzrU}xkyrU|~{~|l#y|r|hz{~k}k{¸x+jm5Ojm}ky5Orh½»WjShkp#nBxrnB¯prpjmhzhzr»WrhzrBxr

~j¬xn~{~}½¹Â½%~smsBk!ì{~U{~x|kzr}kyr|krwj»QnzrÀ»¸È½oxzy|rU{~|l\jUjSUhz{~´mr+Unwlm~jSBn

(14)

NJP "O RN" î9FáA O RN NJP cN

& K

Ü½Ù½Ü

Ô

0>3

àß

! "#!"%$!

Q& T

& ã 8aê Q7?&

T

9-:#%#>

')(*

Ý Ô ß

+!,.-! "#"$!

Q7

T

9-:#>#%

\X{~lm|hzr J#QnqhklmrÈlShon{~er´mrU}z½È½Bnzrn~lSjmhk{~}zy|p

ºy|r|hzjm|~rp ª_r5nm|Uhzrk#|jª"{~$y|jª }kj BOBLn5lmjUj| k}n}k{¸x#jShoUrhk{~|lÄjq»]@

}onqkµU0/jq»«|r SBnU|hn}z{jSQ¹

±

rOrBUrBxrIxjm|z}khonq{~}zOr}½ª_rrÃ}ky|rkr}nzµnqhkr

r||hkrkkraÃUÁn$}nzµÁlShony

°

U{~hkrx}zrÃnmx¬x{¸x\lmhn|yB³wªy|{¸xzy5{%hzjjS}krÃnq}01¿¹ \jmh

rnmxzy#|j|Ur32'jq»i}zy|{~lmhn|yQUª-rUrBBr?J

4 / JU}nzµª-r{~lmyU}ªy|{¸xzy{~|hkjSBjShk}z{jSBn¿}zj$}ky|r%}nkµ 0/-U|honq}k{~jmLS

5 / JUy|r{~lSy}jq»}zy|r|j|UrUrBO|rnq J

5 / G 6 {À» 0/yBn|j$hkrUraxrkzjmh

p#na

798!:;:<

d=;>/

° 5 dS³@?@s:jS}ky|rhkª{~kr

A/ J|Ur|}kyjq»}zy|r%|j|UrUrBO|rnq J

B/ G 6 {À»C2cGN@

p#na

dD

7;8!:9:<

/E=

° d³F?Ls;jS}ky|rhzª{~kr

AG

/

JUª-r{~lmyU}zr#Ur|}zyj»'}ky|r%|j|Ur¬rBB|r¯n J

G/ G 6 4 / {À»H2KGP@

p#na

dID

798:9:<

/E=

° Gd

³@?

4 / jm}zy|rhzª{zr

\|jSh_jS|h«nq~lmjmhz{~}ky|p5}zy|r%}onqkµ$lmhn|ye{~«n\}khzrrmBnqB$}zy|r%}onqkµUnhzrª-r{~lmyU}zr$ª{~}ky

}ky|rU|p$Orh'j»c=Ojn}z{~|l%BjS{U}'jmOrhn}k{~jS|}kyr$Brh½»WjShkp¼}kjxjmpr}krm¹ºnq|~rslS{~´mr

}ky|reª_r{lSyU}'y|r{~lSy}aUr|}zyLnB ª_r{~lSy}zrÄ¬r|}ky j»rnSxky}nkµ »Wjmh+}kyrIp#n}zhk{ÀÁj»

BBlmhkr#¹

Â½$jmho¬rh}kj\{U}zhkj|UBxrw}ky|rr¬Orhz{perU}kr+xzy|rU|~{~|lz}khn}krlm{~rª-rUrBB|rw~r´mr~

j»¿}onqkµUZJS}onqkµU-{n jª ~r´mrOyBna´Sry|{~lmyrh|hz{jShk{~}½+{$}zy|rxzy|rU|~{~|lO¹mºy|rkr%~r´mr~

(15)

e p q s t v y z

4 ` ^ s sSs

5 s s

s

AG m m ^ m m m sa

ºn|~rsJU¾Ãr{~lmyU}Uyr{~lmyU}|Ur|}kyQª_r{lSyU}kr#Ur}kyjq»}kyrnpe|~r|hzjm|~rp"}onqkµU

sm¹-k{~pe|~rjmhUrh

°

³cJ¿neBnhz}k{¸x|¸nh%~r´SrU|p$Orhk{~|l#nkz{~lm|%rnSxkyÃ}nzµ / }kj

}kyr~r´mrF2z¹

|¹ Yjm}k}zjmp0ÈIhkjªk{~|l$jq»}ky|rr{~pe{On}k{~jS}zhkrr

°

³p

J|ranmxzy}onqkµ / {~nzk{ÀÈ

lmre}kjn+~r´mr¿ªy|{¸xky#{~{~}ky|r{lSyU} 5 / ¹

|¹-¾Ãr{~lmyU}zrAYjm}k}zjmp0È

°

³cJOrnmxzy5}onqkµ 0/{~%nkz{~lm|r¯}kj#n$~r´Sr'ªy|{¸xky

{~{~}kwy|r{~lmyU} 5 /o¿nqBe}onzµUª{~}zy|{~I}zy|rnpr%~r´Srnqhkr+jmho¬rhkr¯ª{~}ky#hkrkOrx}

}kj$}zy|r{~hª-r{~lmyU}kr#Ur|}ky AG J 0/Br»Fjmhkr b BG

/ AG

b ¹

^B¹-º'jmUÈ/Yjm}k}zjmp<hkjªk{~|l\j»}zy|r%r~{~p{~Bn}z{~jm}zhkrr

°

³ q

JUranmxzy#}onzµ0/{nzk{ÀÈ

lmre}kjn+~r´mr¿ªy|{¸xky#{~{~}kUr|}ky A/o¹

`|¹-¾Ãr{~lmyU}zr%º'jmUÈ/Yjm}k}zjmp

°

³KJranmxzy}nzµ 0/¿{~'nkz{~lm|r\}kjnr´mrUªy|{¸xzy{~

pIn 1d j e ° d ³ /UnB+}nzµ-ª{~}ky|{~+}ky|rwonqpr-r´mr¿nhzrjmho¬rhkreª{~}ky+hkrkOrx}

}kj$}zy|r{~hª-r{~lmyU}kr#Ur|}ky AG J / Br»Fjmhkr b BG

/ AG

b ¹

¹²-hk{~}z{Óxn¿Bnq}ky

°

³cJU}onqkµU«nqhkrnzk{~lmr$}zj~r´Sr~«nSxxjmhU{~|l+}kj:J

° / ³

° b ³ AG

/ BG

b!

ºy|r%k{~p|~rjShoUrhw{~}ky|r%rnqk{~rk}wk}zhon}zrlme}kj${~prprU}¹qºy|r%BjS}k}kjSp$È½|$k}zhon È

}krlS$oxzy|r¬|~rn}nzµn-kjUjm#n-BjSkk{~|~r%ªy|rhzrn}zy|r}zjmUÈ½Ojm}k}zjmp<jS|rxzy|rU|~r

n$}nkµ5n¸n}zrn\BjSkk{~|~rm¹c\jmh%}kyrkre}½ª_je}krxzy||{&S|raQjShoUrhk{~|l#}ky|r$}nzµ%ª{~}ky{

}ky|r+onqpr%~r´mrUI}zy|r{~h%ª_r{lSyU}kr5Ur|}zyÁp#nahzrUBxr$hkj|xrzkjmh\k}onq~}z{~prmªy|{~r

µmrr|{~|ln$z{pe|~rjShoUrhwpInqµmrn+Or}k}zrh|zrj»~j|xn~{~}½U¹!\Q{~Bnq~US}ky|rxhk{~}k{¸xnqOn}ky

k}zhon}zrlmUUn~kjµU|jªnq_}zy|r]5#"!" !2%jmh:" (" c[ 2 (""05#"L306(V{~-µU|jª$}kj

|hkj|UOxr|rnqh½È½jm|}z{~pInoxzy|rUr ~sa¹

$ %'&

Ã% -,9 \/

$}z{~|jªmª-rUrBBreoxzy|rU{~|l\k}khn}zrlm{~r}zyBn}p#na%{%=B|rBxr~jUnm\Bn¸nOx{~|lB¹

Â½}ky{'zrx}k{~jSQmª-r-hkrOjmhz}jmjS|hKBBhkz}hkrk|~}k-nB\ª_rU{~ox|k{~zk|r-x~jmkr\hkr¸n}zr

}kj }ky|r ÆUÇ

;xjSBxr|}a¹ºª-jÄp#n}zhk{¸xr#npjS|l5}ky|rÃ}zy|hkrrÃª-r5|kr@nhzr»Fhkjmp }zy|r

C)(

æïî 8 <;=@8+* =äî¿ñ:8í*Oäí½êîDFémázê,æçå>=@?ð

- (

(16)

YjUr{~|lqÈ wnhzª_r~QxjS~rax}k{~jm#nBe}zy|r}ky{hejm|r

° sÈk|sa³{~n\honqBUjmpe~lSr|rhn}kra

pInq}khk{ÀQ¹Ou~-j»}kyrpnhkr#hzrjmhUrhkraÄk{~|l}zy|r#p{~|{~pp UrlmhkrrIyr|hk{~z}k{¸x¹#jShkr

Ur}n{~~«nqhkr|hzj´U{Ó¬r${~#}onq|~r|¹

(V230 ) °

C³ °

O³ <Bnqlmr

Æ

g&^ U^ m+m `mS sS

Y-² Æ|Æ

ºÑ+s^ sm m m sSs+ mS

\sÈk|s sm&^ `+ `^ sam+ms |s2`

ºnq|~r!JUº'rz}pInq}khk{¸xr

ºinq|~rnOU^zy|jª}ky|rw}k{~p{~|lhzrk}z«nqB+}kyrrIx{~rBx$jq»Q}ky|rOnhonq~rBxj|Ur

jm|}n{~|r0ª{~}kyIn\yUUBrhx|Orhk||{~|l$Ñu%¨¹ºy|rInqhkrxjSp||}zr+jm#}zy|r%Bnz{-j»

n|hkrzr S|rU}k{¸nqxj|Urmª{~}ky|jS|}«nqUBnqhon~~rQxjS|k}zhkBx}¹

Æ

jmper|hk{~pInqhkxjSBx~|z{jS|nhz{~krw»WhkjSp<}kyrkr+hkrz|~}k$J

'

nÃhkrU{¸x}n|~r5hkrz|~}{~}zyBn}e|k{~|l ~r´mr~e{}zy|rÁr{~pe{On}k{~jSÃ}khkrrÁlShkrnq}k~

{~p|hzj´mr-Orh½»WjShkp#nBxr

°

»Whzjmp ¼}kjS ` jm}zy|r}zrk}wpIn}zhk{¸xr³O

'

rIx{~rOx{~Qp$Bxzy%Or}k}zrhª{~}ky}zy|r! sÈsQp#n}khz{À}kyOnª{~}ky\}ky|r}½ª-jjS}ky|rhk

nO}zy|rxkyrU|~{~|l$yBnqn~pjSk}|j+r¿rx}%ª{~}kye}ky|r¸nq}k}krhpIn}zhk{À

'

}kyr xhk{~}k{¸xnq¿Bn}zyIz}khn}krlmI¬jr|jm}-lm{~´mrwhkrz|~}k%n-lmjUj|njS|rª-jmÓ0yBna´mr

r|Orx}kra¿¹

n}zhk{À

Æ

rmrU}k{¸n s |hkj|xrzkjShk

xj|Ur

Æ Y ¾NY º:Y ¾Lº:Y ²g

Y-² Æ|Æ

ºÑ+s^ m¹~s ^ ^O¹s s¹ s¹`m s^B¹çS s^B¹çm m¹ç

Æ

wg^ m¹~s^ `m¹`S s¹&^ s¹^ ` s^B¹ç&^ s^B¹çm m¹^ ^

\sÈk|s m|sS¹ç ` ¹S ^O¹S `¹~s` `|¹çS `|¹`m ¹çm

ºnr%!J X|rx|}k{~jm¯}k{~pr

°

{~ekrxjSBU³ª{~}zyIU{¿rhkrU}woxzy|rU{~|l$z}khn}krlm{~r

Â½cjShoUrh$}kjÃr||¸n{~ }ky|rzrÁ}½ª-j5Ónqk}$Ojm{~U}ka'ª_r#|rraLnÃUr}n{~~rnBnqUz{+jm

|n}n$nmxxrka¹B¾Ãr%zy|jm|¸BOhkk}wBjS{~}jS|}}kyOn}{~#jmh{pe|~rpr}n}z{jS|Sn~Qxjm~|pe

pj|U{B xnq}k{~jm_nhzrªhz{}z}kr¯{n+|hz{~´mn}kr\´mrx}zjmha¹Bu»W}krh}kyrxjSp|~r}z{~jm$j»-}ky|rA#2)&063

jmOrhonq}k{~jmX}kyrhkrz|~}k{~|l ´mrx}zjmh#{~}zy|r xjm|{~r®}kjÄ}zy|rzyBnhzrL´U{~hk}zBnwprpejmhz

nm|¬hkrz_zBnmxrS¹UÂ½$jm}kyrh_ª-jmhUS}kyr ÆUÇ

{~|zrnq'»WhkrmrU}k~nrrUr0»WjShhkranm

jmOrhonq}k{~jmS||}-jm|~+|rxrzonqhknB+kr»W¿ªhk{~}krwjmOrhonq}k{~jm|nhzrUjm|rw{~${}a¹mºyU|a

»Wjmhn#p#n}zhk{ÀÁj»jmhUrhV@'QjS|~6@ 3+(&/Q0("nhkr#Ujmr${Ã}zy|r Æ¬Ç

hkrlnhU~rk