HAL Id: inria-00074262
https://hal.inria.fr/inria-00074262
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-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Comparison of Accurate Dot Product Algorithms
Jürgen Wolff V. Gudenberg
To cite this version:
Jürgen Wolff V. Gudenberg. Comparison of Accurate Dot Product Algorithms. [Research Report]
RR-2413, INRIA. 1994. �inria-00074262�
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Comparison of Accurate Dot Product Algorithms
J¨urgen Wolff v. Gudenberg Institut f¨ur Informatik Universita¨t W¨urzburg
N˚ 2413
Octobre 1994
PROGRAMME 6
34
56798;:=<?>9@BA?CDE(5FG8;:IH8;6J7K
L
:MONPQN5N#R
4
56
L
:GRS>96TVUWNPQX
Y
:PQCZ8[6\MOP]N
4
U^N#<
4
56J_[H56J7
`ba0c^dWae;f2f2ghji klenm]oJp9mrq0oOsBg\t9uvsxwzy^pZg^{f2cZ|~}gJmxs]q0e;uscWtg\umBc^d;s]oOsBgJmtpZf=}g\avs]y^pZg
`*a0c^vg\um]e^|WsBt
e;ZIcWa0u/|9ga0goOZg\aoOZg+t(9;Iji /oJuOc^Za0gn^;ji^Ie;dWgq
\nI;^aOgoJg\tuvmB Za0c^Ic9qvg|enmBd^c^asuOZf¡¢c^a)u0ZgVe^o\oJpZae£u0g¤oJc^fZpZue;uvsBc^t¥c;¡u0Zg
|9c^uZa0cZ|9pIoJu§¦©¨cWª;W«lIeWq(Gg\g\t=sBf29mBg\f2g\t9u0g|?e£tI|Vf2cZ|WsxwIg|¬sBt=c^a|9g\au0cc^ZuJensBt=u0Zg
GgqvuGcq0q®sB9mBgVenmBd^c^avsBu0Zf¯¡¢c^au0Zg°yWpIe;a0gJm]qu0c9c;mBIcn±³²%´Sus]q)oJc^f2Ie;a0g|¬µsuO?u0Zgc^uOZg\a
µgJmxm¶tZc;µtVenmBd^cWavsBu0ZfqµsBu0VaOgqvIgoJuu0caOpZtuvsBf2g2e;tI|·sBt9u0g\a0f2g|Ws]e;u0g)qvu0c^ae£d^gqvIeWoJg^²(
oJc^tIq¸s¹|9g\aJe;9mBg2sBf2Za0c;º^g\fg\tuc;¡u0ZgIg\a¡¢c^aOfe;tIoJgs]qc^ZuJensBtZg|§e)oJc^f9sBtIe;uvsBc^tc;¡u09s]q
enmBd^cWavsBu0Zf»µsuO§e;tc;m]|c^tZg^²
¼·½¾¿vÀÁz;Â^¬oJc^f2ZpZu0g\a/e£avsBu0Zf2g\uvs]o;{|9c^u0Za0cZ|9pIoJu/oJc^f2ZpZuJe;uvsBc^t
âÄÅ
ÆvÇvÈÉ
Å
ÆbÊbËǸÌQÍÎ
ÏSÐÑÓÒ©ÔÕÖ×ÙØ#Ñ[ÚOÔÜÛ;ÝvÝvÞ/ßn×Ùݸß;Ú0×ÙÝvààná×QÒ©ÞâÚ~ÔÙãSÚvä/ÚOãåÙæå¢çÓèVæÝvÞÞÝvÔvé^ÔÙánßß;Ö×ÙãÙÝvàjÛ\ä/êëå®ëì³ëç
, 2 j')20+,°
½ ½§#c^pIq2}g\u0pI|WsBc^tIq*s]oOsÜpZttZc^pZºWgJm&e[mdWc^avsBu0Zf2gGc^pZa/o\enm]oJp9mBg\amBgZa0cZ|9p9sBu/q0o\enm]ensBa0g
ZaZ}goOs]qg\utZcWpIq~mBgoJc^f2Ie£a0c^tIqe;p9±¤enmBd^c^asuOZf2gqoJc^tZt9pIq\²pZgJm]yWpZgqf2c |Wsxwzo\e;uscWtIq/|9goJg\u
enmBd^cWavsBu0Zf2g§qvc^t9ufs]qvgqg\tpZºa0g§|Ze£tIqjm©e;u0gJmxsBg\a2y^pIe;aOgJm¹qg\ug\t?e;f=}gJmsBc^aOg\tu2ensBtIq®smBgq
Gg\av¡¢cWa0fe;tIoJgq\²
ÁG\¿0½?¬Za0c |9p9sBuq0o\enm]ensBa0g^{Ie£avsBu0Zf2g\uvs]yWpZg(ZaZ}goOs¹qg|9gqc^aJ|WstIe£u0g\pZaq
. /
/ j')b
0Zg§eWo\oJpZae;u0goJc^f2ZpZue£uvsBc^tc£¡°e|9c^uZa0c |9pIoJu21ScWa qtZc^t99f2c^pIq®mB43rqOo\enm]e;aZa0c |9pIoJu65/s]q
gq0qg\tuvs]enmb¡Ùc^afe;t9tpZfg\avs]o\enmZa0c^d^aJe;fq\²G´Stu0ZgtZgJ±Zu(qvgoJuvsBc^tµg q¶^g\uoO¤qvg\º^g\aJenm*e[mdWc7
avsBu0Zf)q¡Ùc^au0Zg(gJ±Ie^oJu/oJcWf2ZpZue;uvsBc^tc£¡Üu0Zgqvg|9c^uZa0cZ|9pIoJuq
8
3:9<;1=
>?
@4ACB
?4DE?
5
c;¡4FIce£uvsBtZd7ÙIc;sBt9ut9pZfIg\aq
B ? { E?
µsBu0e(q¸stZd£mga0c^pZtI|WsBtZdG;{ns²g^²enmxmIsBt9u0g\a0f2g|Ws]e;uOg/a0gqp9muJq
Ienº^g2uOc§IgoJc^f2ZpZuOg|IHJ,,+$ $K#,$) L´Su s]q(cWºWsBc^pIqju0Ie;uu0Zg2aOgqvp9mBuµsmxmIg
|WsNMg\a0g\t9u¡Ùa0c^fu0ZgjpIqvpIenmxmB§oJc^f2ZpZu0g| e;ZZa0cn±sBfe£uvsBc^t
8
3N9
B A K E A O B$P
K E P O QQRQ O B = K E =
µZg\aOg
O S K
|9g\tZc^uOgFIce;ustZd7ÙIc;sBt9u/c^Gg\ae;uvsBc^tIqÓ²
T&saJqvuc;¡ e[mmu0ZgVoJc^f2ZpZue£uvsBc^tc;¡2|9c^pZ9mBgmBg\tZd^u0 Za0c |9pIoJuJq)Ie^qu0c=GgVIg\a¡¢c^aOf2g|
µsBu0ZcWpZu(a0c^pZtI|WsBtZd g\a0a0c^a²´¡ltZc|9c^pZ9mBgmBg\tZd^u0UFIce;uvsBtZd7ÙGc;sBtu ¡¢c^aOfe;u#s¹qjenº[ensxm]e;9mBg^{u09s]q
o\e;tGgIg\av¡Ùc^a0fg|29qv9mxsBu0uvsBtZd)u0Zg¡Se^oJu0cWaqe;tI|oJcWf2ZpZuvsBtZd2Ie;a0us¹e[m³ZaOc |9pIoJuq~c;¡&¡ e^oJuOc^aq
µZg\aOg(e;ubmBge^qvu#Ienmx¡Üc;¡renmxmÜ|WsBd;sBuqe;aOgWV\g\a0cG²$09pIqtZca0c^pZtI|WsBtZd2g\a0aOc^acZo\oJpZaq\²09s]qf2ge£tIq
u0Ie£u2µgIeºWgu0c¬e^|Z|¬Vu0cVhYX^sx¡fe;t9uvs]q0q0e mBg\tZd^uO¬s¹qcZ|Z|UXtpZfGg\aqjsBtIqvu0ge^|%c;¡c^tZg
Za0cZ|9pIoJu2ZpZuu0Zg)Za0c^9mBg\fu0Zg\t s]qja0g|9pIoJg|¬u0cu0ZgoJc^f2ZpZue;uscWtc;¡/eqvpZf§²[ZVgqvZc;µ
u0Ie£usBu/qvp\ oJgq#u0c2oJc^f2ZpZu0gIe;a0us¹e[m³ZaOc |9pIoJuq¡Ùc^ae9sBtIe;a0§qvZqvu0g\f§²
0ZgenmBd^cWavsBu0Zfqµ9s]oO¤e;aOgst9u0a0cZ|9pIoJg|)sBtu0ZgtZgJ±Zu/oOIe;Zu0g\aIeºWgIg\g\t¤|9g\ºWgJmcWZIg|
sBt¬u0Zg¡Ùae;f2g\µc^a0¶ c;¡luOZg¨e;avm]qva0pZZge^o\oJpZae£u0ge;avsBu0Zfg\uvs]o2e;ZZa0ceWo0?¦¨p9m][h9{ܨp9m&^ \«S{
qvg\genm]qvc§¦`_~c^§a«³¡¢c^ae;tc;º^g\a0ºWsg\µj²
ZVguOZg\t?oJc^f2Ie;a0g)u0ZgqvgenmBd^c^asuOZfqe;tI|=e a0goJg\tum¬ZpZ9mxs]qvZg|=f2g\uOZc |¥¦©¨cW§;;«
µsBu0 a0gqvGgoJuu0cuvsBf2ge;tI|?qIe^oJg§oJc^f29mBgJ±9suv^²!ZVg§enm]qvc sBtº^gquvsBde;u0gu0ZgaOgy^p9sBa0g\f2g\t9uq
¡Ùc^aoJcWf2ZpZuvsBtZde^o\oJpZfp9m]e;u0g|¬|9c^u0Za0cZ|9pIoJuq\{³sS²g^²be;tªeW|Z|WsuscWtc;¡eº[e[mpZguOc¤e;t=enmBa0ge^|9
oJc^fZpZu0g||9c^u0Za0cZ|9pIoJu(qvZc^p9m]|GgGg\av¡Ùc^a0fe;9mBg2qvcu0Ie£uu0ZgpZz|Ze;uOg|º[enmBpZge£densBts]qc;¡
c^Zusf)enmre^o\oJpZaeWoJ^²
|9g\uensxmBg|)a0c^pZtI|WsBtZdg\a0a0c^ae;tIenmBZq®s]qc;¡Üqvc^f2g#tZg\µmBZa0cWIcqvg|f2cZ|Wsxwzo\e;uvsBc^tIq~¡Ùc;mxmBc[µq
sBt=qvgoJuvsBc^tZ²G |9gq0oJavsBZuvsBc^t¬c;¡luOZgbT*/ c0 d]]sf9mg\fg\tue£uvsBc^tªe£tI|¤qc^f2g2a0gqp9muJq
c;¡bgJ±ZgoJpZuvsBc^t§uvsBf2gjf2ge^qvpZaOg\f2g\tuJqoJc^tIoOmBpI|9gu09s]qa0g\IcWa0u²
2 j')*"-,./ 012 °! #" $"2%
&')( *+-,.0/2131345476)8:9;+=<
=º^g\aO°q®sBf29mBg^{;ZpZuIc;µg\av¡Ùp9m enmBd^c^avsBu0Zf ¡Ùc^au0ZgoJc^fZpZue;uvsBc^tjc;¡ |9cWuZa0cZ|9pIoJuqf)e;¶^gq&pIqvg
c;¡e(qvc7So\enmxmg|)|9c^ubZa0goOs]q®sBc^t)º[e£avs]e;9mBg/µ9s]oOs]qbIe^q¸s¹o\e[mmBe#mBc^tZd wZ± g|7ÙGc;sBtue^o\oJpZfp9m]e;u0cWa
>¬Gg\a0fsBu0uvsBtZdu0Zgle^|Z|WsBuvsBc^tc;¡Ie;t9/ZaOc |9pIoJuc;¡FIce;uvsBtZd7ÙGc;sBtutpZfGg\aqµsuOZc^pZua0c^pZtI|WsBtZd
g\a0aOc^a1¦© pZf2 ^a { _~c^ ^^£«5 3WmBg\u@?§e;tI|BA)Ig(uvµc FIce£uvsBtZd7ÙIc;sBt9u/t9pZfIg\aq#µsBu0 Ie^qvg@C~{
D |WsBd;sBuq~sBtuOZgfe;t9uvs]q0q0e(e£tI|2gJ±ZIc^tZg\t9uae£tZd^gFEHGJILK
SQ%QQS EHG
B M
²$0ZgZa0cZ|9pIoJu
M
3N9?
D A
Ie^qb
DD |WsBd;sBuqsBt2uOZglf)e;tus¹qOq0eZ²
M
s]qoJc^t9º^g\a0u0g|°sBtu0c(e#wZ±Zg|7ÙIc£st9ut9pZfIg\a~qv9sx¡¢uvsBtZd suJq
fe£tuvs]q0qOemBgJ¡¢uc^abasdWue^o\oJc^aJ|WstZdju0csBuq*gJ± Gc^tZg\t9ulµ#9s¹oOs¹q*sBt)u0Zg/aJe;tZd^g
D
EGJI)K
SQQ%Q S D
EHG
B M
²T&sBtIenmxm u0Zg¤q9s¡Ùu0g|%º[enmBpZg s]q2e^|Z|9g|=uOcVu0Zg¤|9cWu2Za0goOs]q®sBc^t¥º[e;as¹e£9mg2> HJ*,+$
#,$)- J²
D
DON D EHG
B M N DP
EGJI)K
P
NRQ |Wsd£suJqe;a0ga0gyWp9sBa0g|j¡Ùc^abu0Zga0g\Za0gqg\tue£uvsBc^t
c;¡S>({GµZg\a0g Q d^pIe£a|§|WsBd;sBuqje;a0geW|Z|9g|sBtVcWa|9g\a/uOcZa0g\ºWg\tuc;º^g\aFIc;µ(² 0Zg\aOgJ¡¢c^aOg^{g\º^g\t
u0Zgq0yWpIe;a0gT
D
TVc£¡³uOZgm]e;a0dWgqvu!FIce;uvsBtZd7ÙGc;sBtut9pZfGg\aST 9 a Q 1LCVUV 5
DD%D
1)CWUV 5 D CXZY\[^]
o\e;t Ige^|Z|9g|_C$`usfgqµsBu0Zc^pZuc;º^g\akFIc[µj²
aJb]n ³nb¹Á-cbC0ZgmBc^tZd2e^o\oJpZfp9m]e;u0c^afen2GgsBf29mBg\f2g\t9u0g| e^qeº^goJu0cWalc£¡zsBt9u0g\d^g\aqÓ²
#¡¢uOg\a\K e^|Z|WsBuvsBc^tIq~u0ZgsBt9wIt9sBu0gJmB)Za0goOs]qvga0gqvp9mBubs]q~c^Zue[stZg|{ZqvcuOZg°enmBd^cWavsBu0Zf"oOmBge;avmBs]q
mxsBtZge;a²:d;sBtIoJg/µgc^t9mB2e^|Z|jZa0cZ|9pIoJuqsBtIqvu0geW|c;¡ImBc^tZde^o\oJpZfp9m]e;u0c^aq{;uOZgoJcWtIqvue;t9u¡eWoJu0c^a
GgJ¡¢c^aOg(u0Zg@K!s]qtZcWud^a0ge;uOg\aluOIe;t§Z²9°o\oJpZfp9m]e;uvsBtZdq0o\enm]e;aZaOc |9pIoJuqe;a0gc^Zue[stZg| ¸pIqu
9§e^|Z|9uvsBc^tu0cu0Zg(e^o\oJpZfp9m]e;u0c^a²
d^c¤uO9s¹qenmBd^cWavsBu0Zf s¹qe º^g\a0g\ oOsBg\t9uqvc;mBpZuvsBc^t=c£¡uOZgd;sBº^g\t¬Za0c^9mBg\f§² Gc^a0ue£9mg
º^g\aJq®sBc^tc;¡su#pIq®sBtZd2sBt9u0g\d^g\a/e;asuOZf2g\uvs]ou0ce m]e;a0d^ggJ±Zu0g\t9uIe^q~Ig\g\t·sBf29mBg\f2g\tuOg|sBt u0Zg
e# Sf7ghdZa0cW¸goJu¦©`be£c W;«S²
ZVgtZg\º^g\a0u0ZgJmBgq0qlst9u0a0cZ|9pIoJg(uOZg/c^uOZg\a{Wst·¡eWoJulc£m¹|9g\an{ |9cWu0Za0cZ|9pIoJu/enmBd^c^avsBu0Zf)qbsBt u0Zg
¡Ùc;mxmBc[µstZd)Ie;ae£d^ae;ZIq\²
&'Z& /2ii7jk9j)+-,mlnjZ9op<qr5m8$j),7i7q:<
0ZgwIaJqvu/enmBd^c^asuOZf"µ#9s¹oO¤oJcWp9m¹|·d^pIe;ae£tu0g\gtZge;avmB¡¢p9mxmÜZaOgoOs¹q¸scWt¡Ùc^au0Zg(oJc^f2ZpZue£uvsBc^t
c;¡2eUFIce;uvsBtZd7ÙGc;sBtuqvpZf
8
3N9ts
=?
@4A M ?
µe^q ¡¢c^pZtI| ¥`s]o0Ie£u1¸qvg\g=¦©`s]oO ][;« 5²b´Su)s]q
Ie^qg|2c^t)u0Zgc^Iqvg\a0º;e;uvsBc^t)u0Ie;u~pZtI|9g\aoJg\aOuensBt eWq0qvpZf2ZuvsBc^tIqe;Gc^pZuuOZg/a0cWpZtI|WstZdY;/{Wu0Zg
a0g\f)ensBtI|9g\ac;¡u0Zg a0c^pZtI|9g|?qpZf
B O E
µ9s]o0%s]q|9gJwItZg| 9vu 3:9
B N E U 1 B O E 5o\e;t
Gg2a0g\Za0gqvg\t9u0g|e^qe FIc9e;uvsBtZd7ÙIc£st9u(t9pZfIg\a 1SZaOc[ºWs]|9g| u0Ie;utZcc;º^g\aFIc;µ c^apZtI|9g\aFIc;µ
cZo\oJpZaq5²wd^ue;a0uvsBtZdµsBu0u0Zgº;enmBpZgq
M ?
{Geqgy^pZg\tIoJgjc;¡rº;enmBpZgq
M3x
?
s]q/oJcWf2ZpZu0g|e^q*¡Ùc;mxmc;µ/q63
¡Ùc^aIJ3:90K_U?(|9c;µt9u0c(|9c
8
3N9
M ? O M ?O A
u-3N9
M ? N M ?O A U 8
M x?
3:9
8
M x?O A 3:9u
g\tI| ¡¢c^aI
09s]qbtZg\µ qgy^pZg\tIoJgIe^qbuOZgZa0c^Gg\a0uvsBgqbu0Ie£u s M x? 9 s M ? {9e;tI|
M3x
A
s]qe£te;ZZa0cn±9sf)e 7
uvsBc^tc;¡bu0Zg2qvpZf s M ? {Gµ9sxmBg
M xP S D%DD
S M x=
e;a0g(aOg\fensBtI|9g\aq\² g\Ige£uvsBtZd§u0Zgq0e;f2gjZa0c oJgqOq
mBge^|Zqju0c º[enmBpZgq
M
?
pZtI|9g\aoJg\a0uensBt=oJc^tI|WsBuvsBc^tIq
M
A
oJc^t9º^g\a0d^gq u0c§eº;enmBpZgqµsBu0=e;t
g\a0aOc^ac;¡GmBgq0q~u0Ie;tuvµlcpZt9sBuq*c;¡u0Zgm]e^qvu~9m]e^oJgc;¡u0Zgf)e;tus¹qOq0eZ²09s]qe[mdWc^avsBu0Zf+µe^qfc7
|WsxwIg|2e;tI|e;Z9mxsBg|u0coJc^f2ZpZuOgl|9c^uZa0cZ|9pIoJuq&sBt ¦_cW ]]{%_cW ] ^;« 3\pIq®sBtZd(e;te;ZZa0c^Zas¹e£u0g
gqvusf)e;uvsBc^tVc;¡u0Zg2qvpZfc£¡la0g\fe[stI|9g\aJq s =?@ P M ?
{u0ZgjsBu0g\ae;uscWto\e;tVGg2u0g\a0fsBtIe;uOg|¤eWq
qvc9c^tVe^q#u0Zga0gyWp9saOg|Ve^o\oJpZae^oJ·s]qa0ge^oOZg|²hd^goJc^tI|WmB^{sBu(oJc^p9m]|IgZa0c;º^g| u0Ie£u 1Ùsx¡c^tZg
|Ws]qva0g\d9e;a|ZqJV\g\aOcq5ÜuOZgc^Ig\aJe;tI|Zq
M A DD%D
M O A
e£a0gc^a|9g\aOg|2e^o\oJc^a|WsBtZdju0cu0ZgJsBagJ±ZIc^tZg\t9uq
e;tI| sx¡Üuvµc(c^Gg\ae;tI|Zq~c;º^g\avm]e;e^o\oJcWa|WsBtZduOc(u0ZgJsBagJ± Gc^tZg\t9uq\{9u0Zgfe;t9uvs]q0q0ec£¡³uOZgm]e;a0dWg\a
º;enmBpZg¤oJc^t9uensBtIqc^t9mB=|WsBd;sBuq V\g\a0c sBt?u0Zg)c;º^g\avm]e;Z9sBtZd¬a0g\d;sBc^t²J0Zg\a0gJ¡Ùc^a0g^{u0Zg)sBu0g\ae£uvsBc^t
fen2Gg°qu0c^ZIg|e[¡¢u0g\ae;ufcqvu 90K UV/qu0g\Iq~µZg\t e[mmc^Gg\ae;tI|ZqIenº^g#Ig\g\tc^a|9g\aOg|²
´®u°o\e;tGg(Za0c;º^g|)uOIe;u
; =
>?
@CA B
?CD%E?
9<; =
>?
@4A M ?
9<;
M
A
¡Ùc^a/enmxmÜaOgJmg\º;e;t9u/a0cWpZtI|WstZd)f2cZ|9gq;¥e;tI|)¡Ùc^a|9c^pZ9mBg| Za0goOs]q®sBc^tc^Ig\ae£tI|Zq
M ? e;tI|
M A ²
aJb]n ³nb¹Á-cV ZVc^aJqvuÜo\e^qvgbusfgloJc^f29mBgJ±9sBu¸ s]qb1K P
5{enmBu0Zc^pZdW(µgbfen°eWq0qvpZf2g~u0Ie;u
sBt¬d^g\tZg\aenmc^t9mBVuvµcsuOg\ae;uvsBc^tIqe;a0gtZgoJgq0qOe;a0^² _~pZujg\º^g\tVu0Zg\tVuOZg¡ eWoJu0c^as]qja0gJm]e;uvsBº^gJmB
9sBd^§q®sBtIoJge;t eW|Z|WsuscWtµsBu0a0g\fensBtI|9g\a/oJc9qvuqe£umBge^quluOZa0g\gFIc9e;uvsBtZd7ÙIc£st9uc^Gg\ae;uvsBc^tIqÓ²
´Ù¡Üu0ZgstZZpZu#º^goJu0c^aqfpIqvu~Ig¶^g\Zun{^e(uOg\f2Ic^aJe;a0(ºWgoJu0c^ac£¡=K oJc^f2Gc^tZg\t9uq*s¹q~tZgoJgq7
q0e£a0^²09s]q~º^goJu0c^ao\e;tIgpIqvg|)e^q&sBt9u0g\a0f2g|Ws]e;u0gqvu0cWae;d^g*¡¢c^a~u0ZgsBt9wIt9sBu0gJmBZaOgoOs¹qg/a0gqp9mun{
µZg\aOgen¡Ùu0g\auOZgqvpZf2fe£uvsBc^t¥pIqvpIenmxmBfe;t9?a0g\f)ensBtI|9g\aq§e;aOg§gJ±Ie^oJuvmB a=e;tI|¥fen=Ig
|9a0cWZIg|²Z¥Zg\te¶^sBtI|c;¡tZc^a0fe[msVe;uscWts]qle£Z9msBg|{Zqvcu0Ie£ubu0Zga0gqvp9mBuvsBtZdº^goJu0cWaqIenº^g
gJ±ZIc^tZg\t9u(|WsNMg\a0g\tIoJgqtZc^umBgq0q#u0Ie;t u0Zg(fe£tuvs]q0qOejmBg\tZd^u0 D {41¸1 EG
B M U EHGJILK[5 N 5 D oJc^fIc^tZg\t9uqqvp\ oJg 1¸qvg\g( ²B 5²0Zge^|Z|WsBuvsBc^t c;¡bc^tZgº[enmBpZgju0c2u0Ie;ugJ±Ie^oJusBt9u0g\a0Za0g\ue£uvsBc^t
f2ge£tIq/e;t)sBu0g\aJe;uvsBc^t)¡Ùc^au09s]qt9pZfIg\ac;¡*oJcWf2Ic^tZg\t9uq\²
&' n<iqr<S+-,7q:,-9
0Zg\aOggJ±9s]qvuq(e£tZc^u0Zg\ae[mdWc^avsBu0Zf¦¨p9mW][h;«bµ#9s¹oO=c^a|9g\aJqu0Zg qpZf2fe;tI|Zqje^o\oJc^a|WsBtZdu0c
u0ZgJsBabgJ±ZIc^tZg\t9uqe;tI|ju0Zg\tque;a0uq³u0c/e^|Z|°¡¢a0cWf¥mBgJ¡¢ubu0c#avsBd^un{JsS²g^²[que;a0uvsBtZdµsBu0(uOZg9sBd^Zgqvu
gJ±ZIc^tZg\t9u{9pZt9uvsxm³uOZg°|WsNMg\a0g\tIoJgc;¡u0ZggJ± Gc^tZg\t9uq~c;¡u0Zg°qpZf e£tI|2u0ZgtZgJ±ZuqpZf2fe;tI|js]q
m]e;a0dWg\a/u0Ie£t§Z²09s]q/e^|Z|WsBuvsBc^tIe^qu0c2IgjIg\av¡Ùc^a0fg|)µsBu0Zc^pZua0c^pZtI|WsBtZdg\aOa0c^a²0Zg\t u0Zg
qvpZf o\e;tGgoJc^f2ZpZuOg|)§e^|Z|WsBuvsBc^t·¡¢aOc^favsBd^u#u0cmBgJ¡¢un²
aJb]n ³nb¹Á-cbC_~go\e;pIqgc;¡ruOZg°qvcWa0uvsBtZdu0Zg(oJc^f29mBgJ±9suv)c;¡Üu09s]qe[mdWc^avsBu0Zf»o\e;t)tZc^uIg
Gg\u0u0g\au0Ie£t 1 K D
mBc^dK1 K[5 5²pZavsBtZd2uOZg(qvc^a0uvsBtZdZIe^qvgjº[enmBpZgq#µsBu0u0Zg(q0e£f2g/gJ±ZIcWtZg\tu
e;aOg/e^|Z|9g|²:d^ce º^goJu0c^abc;¡f2c9qvuvmB+1 EHG
B M
UWEHGJILK[5 N º;enmBpZgqIe^q*u0cIgqvu0c^aOg|²^densBt
u0Zg(eW|Z|WsuscWtc;¡Üc^tZgt9pZfIg\af2ge;tIqe£t2sBtIqvg\a0uscWt)stuOIe;uº^goJu0c^ae;tI|)e;t§e^|Z|WsBuvsBc^tc;¡benmxm
sBuqoJc^f2Gc^tZg\tuJq\²
TZc^a|9g\uensxmBg||Ws]q0oJpIq0q¸scWtc;¡u0Zgqvg|9c^uZa0cZ|9pIoJule[mdWc^avsBu0Zfq~e;tI|2aOgJm¹e£u0g|2ZaOc^9mBg\fqqvg\g
g^²dG²¦`_~c^§a;«®²
&' h9+-<qV<q <+ 13q qri 45m5m8$,7i
bg\a0 a0goJg\tum^{b¨c^ZGgJmBuIeWqZpZ9mxs]qvZg|?e·tZg\µ"|9c^u0ZaOc |9pIoJuenmBd^c^avsBu0Zf ¦©¨c^§£[«~µ9s]o0
pIqvgqjqvue;tI|Ze£a| ´ f7ff FIce;ustZd7ÙIc;sBt9u(c^Gg\ae;uvsBc^tIq u0c§em]e;a0d^ggJ±Zu0g\tu(e£tI|sBt9u0g\a0f2g|Ws]e;uOgJm
qvuOc^a0gqu0Zg(qpZf2fe;tI|Zq~sBteue;9mBg(µsuO1 EG
B M U EHGJILK N 5 oJc^f2Gc^tZg\tuJq\²
09s]qenmBd^c^asuOZf+µ9s]oOIe^qZaOc[ºWg\t2u0cIg#º^g\a0j¡eWqvus]q|9gq0oJavsBGg|st)|9g\uensxmIsBt)u0ZgtZgJ±Zu
qvgoJuscWt²
#,0 ® "2 &(')*"-,./ 012
0ZgenmBd^c^asuOZfµ9s]oO¬s¹q°¡¢cWa0fp9m¹e£u0g| ¡Ùc^a(9sBtIe;a0¬e;avsBu0Zf2g\uvs]ofsBfs]o\qu0Zg2ZaOc oJg|9pZa0g)c;¡
u0Zg # @h K ,enmBd^c^avsBu0Zf»e£tI|§oJc^tIq®s]qvuJqc^pZuc;¡ZIe^qgq\²
')( o78 q (
0ZgqvpZffe;tI|Zqµ9s]oOe;a0g~Ie;a0uvs]enmZZa0cZ|9pIoJuqa0g\Za0gqvg\t9u0g| sBt2pIqvpIenmFIce;ustZd7ÙIc;sBt9u¡¢c^aOfe;u
e;aOgstIqg\a0u0g|)sBteue;9mBg^{qvcu0Ie;uu0Zg(qpZf c;¡enmxmÜue;9mBg(g\t9u0avsBgq~s]q#u0ZggJ±Ie^oJu/|9c^u0ZaOc |9pIoJu²
0c mxsBfsBuu0Zg§q¸s:V\g c;¡/u0Zg)ue;9mBgu0cVeVoJcWtIqvue;t9u(µg§|Ws]qvuvsBtZd^p9s]qv Ig\uvµg\g\t c |Z|~e;tI|
g\ºWg\t FIc9e;uvsBtZd7ÙIc£st9ut9pZfIg\aqeWo\oJc^a|WsBtZd2u0cu0ZgJsBam]e^qvu9sBu²09s]qZa0cWIg\a0uv)c;¡ÜetpZfGg\a
s]qo\enmxmg|·sBuqdWg\tpIq\²
ZVgu0Zg\t§pIqgu0Zg¡Ùc;mxmBc[µstZd)Za0c^Gcq®sBuvsBc^tIqe£Ic^pZuu0Zg(e;avsBu0Zfg\uvs]o;²
°|Z|WsBuvsBc^t)c;¡u¸µct9pZfIg\aq*µsBu02u0Zg/qOe;f2ggJ± Gc^tZg\t9ule;tI|uOZg/q0e;f2gd^g\t9pIqs]q~gJ±Ie^oJu²
°|Z|WsBuvsBc^tc;¡u¸µct9pZfGg\aq#µsBu0u0ZgqOe;f2ggJ± Gc^tZg\tue;tI|·c^ZIcq¸suOg(q®sBd^ts]q#gJ± e^oJun²
0Zg(qvpZf2fe£tI|Zqle£a0gsBtIqvg\aOu0g|)sBt§e;te;a0aenµsBu0§1 EG
B M
U2EGJI)K N 5a0c;µ/qÓ{^c^tZg¡Ùc^a
ge^oOgJ±ZIc^tZg\t9u/e;tI|oJc;mBpZf2tIq\{ c^tZg¡Ùc^age^oOd^g\t9pIq\²9´Ù¡Üu0ZgmBcZo\e;uvsBc^tµZg\aOgu0ZgtpZfGg\a
s]quOcGgsBtIqvg\a0u0g| s]qcZo\oJpZ9sBg|VµsBu0Ve)tZc^tV\g\aOcº[enmBpZg2c^asBuqoJcWa0a0gqvGc^tI|Ze;t9u(e^|Z|9a0gq0q#¡Ùc^a
u0Zg(|WsNMg\a0g\t9ud^g\tpIq#oJc^tuJensBtIqlejº;enmBpZgc;¡Üc^ZGcq®sBu0g(q®sBd^t{Ze;tgJ±Ie^oJue^|Z|WsBuvsBc^t)s]qIg\a¡¢c^aOf2g|
e;tI|·u0Zga0gqvp9mBuvsBtZdqvpZf-s¹qlstIqg\a0u0g|)sBt u0Zg(ue£9mg^²
u/uOZg(g\tI| c;¡u09s]qZIe^qvgu0ZgqvpZf c;¡lenmxmbue;9mBgg\tuOavsBgq#s¹qgJ±Ie^oJuvmB u0Zg(µe;t9u0g|§qpZf
e;tI|¬uOZgue;9mBg¤o\e;t=GgZa0cZoJgq0qvg|¬sBt=u0ZgcWa|9g\a2c;¡/uOZggJ± Gc^tZg\tuJq\{¡Ùc^age^o0=gJ±ZIcWtZg\tu
u0Zg\aOge;a0g(e£ulfcqvug\t9u0avsBgq\²
aJb]n ³nb¹Á-cb\f~e^oOe^|Z|WsBuvsBc^t¬sBt=u09s]qjZIe^qvg)a0g|9pIoJgqu0Zg)tpZfGg\ac£¡/ue;9mBg)g\tu0asgqÓ²
09pIqGgq®s]|9gqu0ZgsBtIqvg\aOuvsBc^tVsBt9u0c§uOZg2ue;9mBg2tZc c[ºWg\a0Zge^|·s]q(ZaOc |9pIoJg| µsBu0Va0gqIgoJuu0c
u0Zgja0c^pZtI|9g| oJc^f2ZpZue;uscWtc;¡Üu0ZgqvpZf§²
´Ù¡z|99tIe;fs]o~f2g\f2c^a0fe;tIe£d^g\f2g\t9us]qbeº;ensxm]e;9mBg^{;u0Zglq®sV\gc;¡Iu0Zg~ue;9mBgf)eIga0g|9pIoJg|
gJsBu0Zg\a %suJq)c^a0de;t9sVe;uscWt eWqeVIe^que;9mBg^{c^a)¥enmxmBc o\e;ustZd¥qvu0c^aJe;d^g§cWt9m%¡¢cWau0Zg
e^oJuOpIenmxm¬pIqvg|¬ae£tZd^gc£¡/º[enmBpZgq2|9g\Gg\tI|WsBtZd=c^tuOZgfsBt9sBfenme;tI|Vf)en±sBfe[mgJ±ZIcWtZg\tuqÓ²
d;sBtIoJgu09s]q³sBtIoJa0ge^qvgqa0pZt9uvsBf2ge;tI|°s¹qenm]qvce;Z9mxs]o\e;9mBg/u0c#u0ZgbmBc^tZde^o\oJpZfp9m]e;u0c^abenmBd^c^avsBu0Zf {
µg(|9c2tZc^u#gJ± 9mBc;sBuu09s]qc^ZuscWt¡ÙpZa0u0Zg\a²
_gJ¡Ùc^a0gµgoJc^f2gu0cu0ZgcWu0Zg\aZIe^qvgq\{µgµe;tuju0cV|9gq0oJavsBIgu0Zg§oJcWf2ZpZue;uvsBc^t¬c;¡
|9c^pZ9mBgjmBg\tZd^u0 Za0c |9pIoJuJq~sBt§f2c^aOg(|9g\uensxmS²
'Z& +-46LqO6Lq:,7.$9om5 476Z9;j 76)jL138:9jL+-,
0&coJc^fZpZu0g/e(|9cWpZ9mg7QmBg\tZd^uOZa0c |9pIoJu~sBt)u0ZgpIqvpIenmKFIce;uvsBtZd7ÙGc;sBtu*¡¢cWa0fe;u
M
e;tI| e£a0g
qv9mxsBusBtuOc2IenmBº^gq\{9sx¡fe£tuvs]q0qOejmBg\tZd^u0s]qcZ|Z|uOZg(qvgoJc^tI|Ie[m¡c£¡ s]q/qv9mxsBue;densBt² 09s]q
µc^p9m]|aOgqvp9mBusBtsBtIqvg\aOuvsBtZd hIe£a0uvs]enmZa0cZ|9pIoJuqsBt9u0c2u0ZguJe;9mBg^²
^²qv9mxsBu
M 9 M N M 9G N 9
99Z N ^
Z²~sBtIqvg\a0u
M
G
S M
9Z
S M
^
S M
I
S M
9Z
S M
9^
0Üe;¶WsBtZdu0Zg2d^g\t9pIqc;¡u0ZgtpZfIg\aJqsBtuOc§e^o\oJc^pZt9u¡¢c^au0Zg2IeWqvg CI9 uOZg2tpZfGg\a
c;¡bIe;a0us¹e[m³ZaOc |9pIoJuqo\e;tGg(a0g|9pIoJg|·u0cI{Ws¡Gc^u0)¡Se^oJu0c^aJqle£a0gg\º^g\t{Ie;tI|)uOc {9sx¡rc^tZgcWa
Gc^u0¤e£a0gc |Z|²
^²~sx¡
M
e;tI| e;aOg/cZ|Z|{zq9msBu
M
sBt9u0cWG
8 E 1 M 5 e;tI|
M
9
M U G 8 E 1 M 5
µZg\a0g@G
8 E 1 M
5J9 a Q D Xk]
= X
= ]
sBtIqvg\a0uG
8 E 1 M 5
Z²gJm]qvg
M
9
M
Z²qv9mxsBu
M
9
M
^ N M
n
-9G N 9
I²~sBtIqvg\a0u
M
^G
S M
^9
S M
G
S M
9
0Zg2qvpZZu0ae^oJuscWt e£tI|§fp9mBuvsB9mxs]o\e;uvsBc^t st¬qvu0g\=e£a0ggJ± e^oJun{zq®sBtIoJg2Gc^u0g\t9u0avsBgqIenº^g
u0Zg)q0e;f2gjgJ± Gc^tZg\tue;tI| c^tZgs]qe)Ic;µg\ac;¡u0ZgIe^qg^²´Ù¡Ic^uO
M
e£tI| e;a0gc |Z|{
M
s]qg\ºWg\t{zq®sBtIoJg2cWtZg9sBu s¹qo\e£tIoJgJmmBg|{Zg\tIoJgjsBtqvu0g\V)e;umBge^quc^tZgtpZfIg\as]q g\º^g\tVe;tI|
µsxmxmluOZg\a0gJ¡¢cWa0gIgqv9mxsBusBt9u0c§)Ie;a0uJqge^oOc;¡lµ#9s¹oOVIe^q 9
D
[ |WsBd;sBuq\²#c^u0gu0Ie;u#st
u09s]qo\eWqvg° 9 D U¬(²0ZgZa0cZ|9pIoJuq*sBt§qvu0g\)uOZg\a0gJ¡¢cWa0g/Ienº^ge;uf2cqvu D |WsBd;sBuq#e;tI|e£a0g
oJc^fZpZu0g|gJ±Ie^oJuvmB^²
/tZc^uOZg\alenmBu0g\a0tIe£uvsBº^g/oJc^p9m]|)Ig#u0coJc;mxmBgoJuu0ZgIe;aOuvs]enmzZa0cZ|9pIoJuqrst)uvµcFIce;uvsBtZd7ÙGc;sBtu
t9pZfIg\aqa0g\Za0gqvg\t9uvsBtZdVu0Zg§e£ZZa0cn±sBfe;uOga0gqvp9mBue;tI|¬u0ZgaOg\fensBtI|9g\a e£tI| stIqg\a0uuOZgqvg
uvµcI²
^²qv9mxsBu
M 9 M N M 9G
N
9
99Z
N
^
Z²
8
3:9
M K
Z²mu 3N9 1 1 1 1 M
G 8 5 O M
5
O M I 5 O M
9Z 5 O M
9^
I²~sBtIqvg\a0u
8
e;tI|Bu
09s]qµc^p9m]|)a0g|9pIoJgu0ZgjtpZfIg\a#c;¡ue;9mBgsBtIqvg\aOuvsBc^tIq\{GZpZu/q®sBtIoJg2e;tsBtIqvg\a0uscWts]q/e)oOZge;
c^Gg\ae;uvsBc^t{ µlg(|Ws]| tZc^u~sBf29mBg\f2g\t9uu09s]qº;e;avs]e;t9u²
0Zg~¡¢c;mxmBc;µsBtZdqv9mxsBu0uvsBtZdjZa0c oJg|9pZaOglµ#9s¹oO2c^t9mBjtZg\g|ZqcFIce;ustZd7ÙIc;sBt9ule;avsBu0Zfg\uvs]oZaOc7
|9pIoJgqe 7S|WsBd;sButpZfGg\a
M
+e£tI|e D U §|WsBd;sButpZfIg\a
M
{Zµ#Zg\a0g2 D U=
qv9mxsu-1
M S M S M
b5
3:9 1LC
N 5 K M
M
3N9
1 M 5
M 3N9
M M
09s]qenmBd^cWavsBu0Zf s]qoJcWa0a0goJu¡Ùc^ae;t?e£a09sBu0ae;a0¬f2c^tZcWu0c^tZga0c^pZtI|WsBtZdI{*sx¡e;avsBu0Zf2g\us¹o\e[m
c^Gg\ae;uvsBc^tIqe£a0g(c^Zusf)enmxm|9gJwItZg|²´®u°o\e;tVenm]qvc)IgpIqvg| u0c|9g\u0g\a0f stZgu0Zgd^g\t9pIq#c;¡
M {
µZg\tqvg\u0uvsBtZd 9 D
U=+e;tI|)u0gquvsBtZd
M ¡¢cWa"V\g\aOcI²
`ba0c9c;¡Sqf)e)Ig ¡¢cWpZtI|st¬¦gGsBt ^ \«
´Ù¡luOZg(g\º^g\t Ie;a0uc;¡le2t9pZfIg\as]q#tZg\g|9g|{µ9s]oO§sBtI|9g\g| s]qu0Zgo\e^qvg stu0Zgc^asd£stIe[m
enmBd^cWavsBu0Zf ¦©¨c^§;^«®{
M
¥Ie^q~u0c(Gg°o\enm]oJp9m]e;u0g|eWqle u0a0pZtIo\e;uscWtµ9s]oO)sBtu0pZaOt2wZ±Zgq~u0Zg
a0cWpZtI|WstZd)f2cZ|9g3
3:9 1LC
N 5 K M
M
3N9
1 M 5
µZg\a0gc^Ig\ae£uvsBc^tIq~µsBu0
e;a0gu0a0pZtIo\e£u0g|e£tI|2µsBu0 ¥e;a0ga0c^pZtI|9g|enµe ¡¢aOc^f V\g\a0cG²
´Ù¡u0Zg)m]eWc^pZuc;¡ e FIce;uvsBtZd7ÙGc;sBtu2t9pZfIg\as]q wZ± g|{~e^q ¡¢c^au0Zg´ ff7f ¡Ùc^a0f)e;u{g^²dG²B{
qv9mxsBu0uvsBtZd¬c;¡/et9pZfIg\a2fenf2c^aOg2g\ oOsBg\tum¬Ig)sBf29mBg\f2g\t9u0g|¬9VgJ±Z9mc£sustZd 9su wIgJm¹|
c^Gg\ae;uvsBc^tIqÓ²
' o78 q &
´®t¤ZIeWqvg22u0Zgjg\tuOavsBgqc;¡u0Zgue;9mBge£a0g(u0aJe;tIq®¡Ùc^a0f2g| stVqvpIoOVe2µen)u0Ie;uenmxmrIenº^gju0Zg
q0e£f2g2q®sBd^t² 09s]qjo\e;tIge^oO9sBg\º^g|µsBu0ZcWpZuoOIe;tZd;sBtZdu0ZgqvpZf c£¡lu0Zgue;9mBg2g\t9u0avsBgq
u0ZgjgJ± 9mBc;sBue£uvsBc^t§c;¡bc^tZgc;¡bu0Zg¡Ùc;mxmBc[µstZd¡Ùc^a0fp9m]e^q
M N 3N9
B Y O U E Y 9 A
>?
@
B Y O ? N 1 B U E 5¸
Y
M N 3:9
B Y O U E Y 9 A
>?
@CA B Y O ? N 1¸
B U E 5¸ Y
µZg\aOg
M
e;tI| +e;a0g#u¸µce^|neWoJg\tu~ue;9mBg/g\t9u0avsBgq~µsBu0|WsNM³g\aOg\tuq®sBd^t²:d;sBtIoJg(gJsBu0Zg\a
B U E c^a
B U E
Ie^q~u0Zgq0e;fg°q®sBd^te^q
B
µg/o\e;tf2cZ|Wsx¡¢2uOZg/ue£9mg92a0g\9m]e^oOsBtZd
M
e;tI|
u0ZgqvpZf2fe£tI|Zqc;¡bu0ZgavsBd^9uIe;tI|§q¸s¹|9g^²
¡Ùu0g\a)u0Zg suOg\ae;u0g| e;Z9mxs¹o\e£uvsBc^tc;¡u09s]q2c^Gg\ae;uvsBc^t¥u0c=enmxmIensBaq)c;¡e^|n0e^oJg\t9uue£9mg
g\t9u0avsBgqjµsBu0|WsNMg\a0g\t9uq®sBd^t ¡¢aOc^f 9sBd^uOc)mc;µ gJ± Gc^tZg\tuJq(enmxmlº;enmBpZgq st¬u0Zg2uJe;9mBg2Ienº^g
u0Zg)q0e;f2g2q®sBd^t² d;stIoJg)u0Zg2fp9mBuvsB9mxs]o\e;uvsBc^tIqµsBu0¬e)Ic;µg\ac;¡lu0ZgIe^qvge^qµgJmxmeWqu0Zg
e^|Z|WsBuvsBc^tIq)µ#9s¹oOe;a0ge^oJu0pIenmxmB?Gg\av¡¢cWa0f2g|?e£a0g§a0cWpZtI|WstZd=g\aOa0c^a¡Ùa0g\g^{~u0Zg§º;enmBpZg¤c£¡(u0Zg
|9c^uOZa0c |9pIoJuqvuvsxmxms¹q#u0ZggJ±Ie^oJuqvpZf c;¡enmxmruJe;9mBgg\tu0asgq#µ9s]oO¤tZc;µ¥sBt u0pZa0t§enmxmbIeºWgu0Zg
q0e£f2g(q®sBd^t²
d^cuOZg°q®sBd^tc£¡re|9c^u0Za0cZ|9pIoJufen2ge^q®sxmBGga0ge^| ¡¢aOc^f+u0ZguJe;9mBg^² 09s¹qc^Ig\ae£uvsBc^t2s]q
ZgJmB9¡Ùp9mb¡¢c^aoJc^fZpZue;uvsBc^tc;¡bIcWpZtI|Zq\²
c^uOg^{Zc;µg\º^g\a{uOIe;u(u0Zg)t9pZfGg\ac;¡°qvpZf2f)e;tI|Zqjfen¤Gg§oJc^tIq®s]|9g\ae;9mB sBtIoJa0ge^qvg|²
T c^a2u0Zg§qvpZZuOae^oJuvsBc^t=c;¡u0Zg§q0yWpIe;a0gc;¡u0Zg§qvfe[mmBgqvutpZfIg\a ¡¢a0cWf uOZg¤q0yWpIe;a0g)c;¡u0Zg
m]e;a0dWgqvu/t9pZfIg\a{g^²dI²B{9Ienmx¡lc£¡ru0Zgjue;9mBg^{ s²g^²Ic^tZgjg\tuOa02¡Ùc^ageWo0 gJ± Gc^tZg\tun{ze;aOgwZmxmBg|sBt²
0Zg\aOgJ¡¢c^aOg§µg)sBtº^gquvsBde;u0g| qvc^f2g§enmBu0g\aOtIe;uvsBº^gqµ9s]oO e;aOg§Za0gqvg\t9u0g| sBt¥u0Zg)¡Ùc;mxmc;µsBtZd
oOIe;Zu0g\a²
' o78 q
´®tZIe^qg ·u0Zg2ue;9mBg)g\tuOavsBgq(e;a0g)e^|Z|9g|¡Ùa0c^f!mBc[µ u0c9sBd^¬gJ± Gc^tZg\tuJq\²J0Zg¡Ùc;mxmc;µsBtZd
enmBd^cWavsBu0Zf»dWpIe;ae;t9u0g\gqea0c^pZtI|WsBtZd)g\a0a0c^a~mBgq0q#u0Ie;t§p9mBIqj¦©¨c^§;W«S²
¡Ùc^agJ±Z 3N9¥mBc;µu0c9sBd^
sx¡gJ±ZIc1¸qpZfG5¥gJ±Z§u0Zg\t
e;p9± 3N9fe;¶Wg g\º^g\t41uJe;9mBg^¦gJ± {c |Z|9«5
qvpZf 3:9 qvpZf
O
1¸e;p9±
O
ue;9mBg^¦gJ±Z{g\º^g\tZ«5
gJm]qvg
qvpZf 3:9 1¸qvpZf
O
ue;9mBg^¦gJ±Z{cZ|Z|9«5
O
ue;9mBg^¦gJ±Z{g\º^g\tZ«
g\tI| s¡
g\tI| ¡¢c^a
' j 134 j)+-,
0Zg#a0pZtusfgoJcWf29mBgJ±sBuvc;¡zu0ZgµZc£mgenmBd^cWavsBu0Zf s]q 1 K 5b²;#mmIcWIg\ae;uscWtIqe;a0gqvue;tI|Ze£a|
FIce£uvsBtZd7ÙIc;sBt9uc^Ig\aJe;uvsBc^tIq\{qvc)u0Zg¡Se^qvu FIc9e;uvsBtZd7ÙIc£st9uIe;a|9µe;aOgfenGgpIqg|² gqv9sBu0g
u0Zg wZmm7QsBt st ZIe^qvg2)u0Zgj¡ eWoJu0c^a#¡¢c^auOZg qpZf2fe;uvsBc^tc;¡uOZg2ue;9mBgpIqvpIenmxmB s¹q tZge;avmB=^²
pZgu0cu0Zg|9c^pZ9mBg7Qmg\tZdWu0¤o\enm]oJp9m]e;uvsBc^tc£¡ÜZa0cZ|9pIoJuq~u0Zg/gJ±ZgoJpZuvsBc^tuvsBf2g#s]qIg\uvµg\g\t ^K
e;tI|¥%aK FIce;uvsBtZd7ÙGc;sBtu2cWIg\ae;uscWtIq21Sfp9mBuvsB9ms]o\e;uscWtIqe;tI|=eW|Z|WsuscWtIq59mBpIq2e oJc^tIqvue;t9u
c;º^g\a0ZgeW|²´Ù¡0{Zc[µg\º^g\an{u0ZgVenmBd^c^avsBu0Zfs]quOc=IgoJc^fIe;a0g|¥µsBu0 u0ZgpIqvpIenm(a0c^pZtI|9g|
enmBd^cWavsBu0Zfu0ZgjsBtI|9gJ±ªoJc^fZpZue;uvsBc^tIq#¡Ùc^au0Zg2ue;9mBgsBtIqvg\aOuvsBc^tVfentZc^uGg2tZg\d;mBgoJu0g| c^t
f2cZ|9g\a0toJc^f2ZpZu0g\aqÓ{Ie^q~µgµsxmmqvg\g ¡¢a0cWf"cWpZaf2ge^qvpZaOg\f2g\tuJqZa0gqvg\t9u0g|)sBto0Ie;ZuOg\aW^Z²
0Zg¤e;fc^pZtuc;¡qvu0c^aJe;d^g)u0c¶Wg\g\?u0Zg·st9wIt9sBu0gJmB¥Za0goOs]qvgVaOgqvp9mBu2s]qa0gJm]e;uvsBº^gJmB?9sBd^{
1 EG
B M U EGJI)K
N 5=t9pZfGg\aq\{Ie[muOZc^pZd^sBt fe;t9e;Z9mxs]o\e;uvsBc^tIqe2qvf)enmxmg\aº^goJu0cWalµsmxm
qvp\oJg^²
0Zge^o\oJpZfp9m¹e£uvsBc^t2c;¡ze;t2e^|Z|WsBuvsBc^tIe[mzº[e[mpZg#f2ge;tIq&sBuq&sBtIqvg\a0uvsBc^t st9u0cu0Zgue£9mg1SZIeWqvg
5J{Zu0Zg(e^|nvpIqvu0f2g\t9uc;¡q®sBd^tIq\{ sx¡rtZgoJgqOq0e;a01SZIeWqvg5e;tI| wItIenmxmB§u0ZgtZg\µ oJc^f2ZpZue£uvsBc^t
c;¡bu0Zg(qvpZf c;¡re[mmbue;9mBgg\t9u0avsBgq(1SZIe^qvg(5J²
j')~
#,0 S "#³ (')b+-,./ 012
´®tVu09s]qqvgoJuvsBc^tµg|9gq0oJasGgqvc^fg(f2cZ|Wsxwzo\e;uvsBc^tIqc£¡l¨c^ZIgJmBu ©q cWu0Za0cZ|9pIoJumBd^c^asuOZf
µ9s]oO§Ienº^gGg\g\t§sBf29mBg\f2g\t9u0g| stc^aJ|9g\aluOc
sBtIoJa0ge^qvge^o\oJpZae^oJ
a0g|9pIoJg(aOpZtuvsBf2g
a0g|9pIoJgqu0c^ae;dWg/a0gyWp9sBa0g\f2g\t9uq
¡eWoOsmxsBue;uOge^o\oJpZfp9m]e;uvsBc^t
')( /2ii7jk9j)+-,mlnjZ9o q:5m8$jL,i7qr<_jL, o78 q
0Zg fen±9sf)enm(a0c^pZtI|WsBtZd¥g\a0a0c^a§oJcWf2fsBu0u0g|%sBt ZIeWqvg s]q§%p9mIqÓ²´Ù¡2µga0g\9m]e^oJg¬u0Zg
e^|Z|WsBuvsBc^t=c£¡lu0Zg)ue;9mBg2g\t9u0avsBgqju0Zg ¡¢c;mxmBc;µsBtZdVenmBd^c^avsBu0Zf§{&u09s]qg\a0aOc^as]q(oJcWf2ZpZu0g| st
u EG e;tI|e;tpZ|Ze;u0g(c£¡ru0ZgaOgqvp9mBu
8
?rG s]qGcq0q®sB9mBgu0cc^ZuensBt¬p9mB¤e^o\oJpZaeWoJ^²
¡Ùc^agJ±Z 3N9¥mBc;µu0c9sBd^
sx¡gJ±ZIc1¸qpZfG5 gJ±Z§u0Zg\t
e;p9± 3N9fe;¶Wg g\º^g\t41uJe;9mBg^¦gJ± {c |Z|9«5
1¸e;p9±{a 5"3N9 e;p9± N uJe;9mBg^¦gJ± {g\º^g\tZ«
1¸qvpZf {a5 3N9 qvpZf
N
e;p9±
gJm]qvg
1¸e;p9±{a 5"3N9 qvpZf N ue;9mBg^¦gJ±Z{cZ|Z|9«
1¸qvpZf {a5 3N9 e;p9±
N
ue;9mBg^¦gJ±Z{g\º^g\tZ«
g\tI| s¡
a0g\f 3N9a
O
a
g\tI| ¡¢c^a
¡Ùu0g\au0Zg¡Ùc^amBc9c^qvpZf e;tI|a0g\f o\e;tIge^|Z|9g|Ve;tI|VqpZZu0ae^oJu0g| u0ca0goJgJsBº^ge·c^tZg
p9mBVe;ZZa0cn±9sf)e;uvsBc^tc^a/eqvIe£a0sBtIoOmBpIq®sBc^tc;¡bu0Zga0gqvp9mBu²
fe^oOe^|WsBuvsBc^tµsBu0a0g\f)ensBtI|9g\a{Zc;µg\º^g\a{noJcqvuq/q¸sf9mge^|Z|WsBuvsBc^tIqbe;tI|uOZg\a0gJ¡¢cWa0gu09s]q
º;e;avs]e;t9us]q|9g\Ie;uJe;9mBg^²I´®us]qu0c9c2q®mBc;µu0c2Gge;uu0Zg mcWtZde^o\oJpZfp9m]e;u0c^asBf29mBg\f2g\t9ue;uscWt²
'Z& 2q 76L8$13q o78 q &
´®tZIe^qg)u0Zg2t9pZfIg\a(c£¡lue;9mBg)g\tuOavsBgqs]qsBtIoJa0ge^qg|sBt¬d^g\tZg\aenmS²´Sujfen§Gga0g\9m]e^oJg|
9Veo0Zge;Gg\a(Za0cZoJg|9pZa0g)µ9s]o0¬oJc^f2ZpZu0gqje)a0c^pZd^e£ZZa0cn±sBfe;uscWt¤c£¡lu0ZgqpZfc;¡u0Zg
ue£9mgg\t9u0avsBgq\{qvc¬u0Ie;u)u0c^uJenm°o\e;tIoJgJmxm]e;uvsBc^t¥s]qenº^c;s]|9g|%sBt¥ZIe^qvgVZ² 09s]q)Za0c oJg|9pZaOg§s]q
u0ZgVe^|Z|WsBuvsBc^t¥c;¡(uOZg¤uJe;9mBg¤g\t9u0avsBgq¡Ùa0c^f9sBd^¥u0c mBc;µ»gJ±ZIc^tZg\t9uq)pZt9uvsxm(u0Zg§gJ±ZIcWtZg\tu
|WsNMg\a0g\tIoJg2Gg\u¸µg\g\tu0Zg2qvpZf e;tI| u0ZgtZgJ± ug\t9u0a0)s]qd^a0ge;uOg\a/u0Ie£t ² 09s]q(oJc^aOa0gqvIcWtI|Zq
u0cu0Zge^|Z|WsBuvsBc^t¬¡Ùa0c^f!mgJ¡Ùuu0c§asdWujsBt=u0ZgenmBd^c^avsBu0Zf µ9s]oO?qvc^a0uq u0ZgqvpZf2fe;tI|ZqÓ²´St
¦©¨p9m!][h;«ZsBu*s¹q~qvZc;µt2u0Ie£uu0ZgaOg\fensBt9sBtZd qpZf2fe;tI|Zq*fentZcWubu0c^uenmxmB2o\e;tIoJgJmu0Zga0gqp9mun{
sx¡/u0Zg)gJ±ZIc^tZg\t9u2|WsMg\a0g\tIoJgs]qjd^a0ge;u0g\aju0Ie;t ² d;sBtIoJgµg2fenIeºWgg\t9u0avsBgq ¡¢cWa(ge^oO
gJ±ZIc^tZg\t9uµgIeºWgu0ca0g\9m]e^oJgu09s]q9Z²0Zg°eW|Z|WsuscWt)¡¢a0cWf+mBgJ¡Ùuu0cavsBd^un{^Zc;µg\º^g\a{^IeWq
u0cjIgGg\av¡Ùc^a0f2g|µsuOZc^pZua0cWpZtI|WstZdg\a0aOc^a{Ósu|9g\u0g\a0fsBtZgq~u0ZgcWa|9g\ac;¡fe;d^t9sBu0pI|9g#c;¡u0Zg
qvpZf e;tI|)d;sBº^gqeja0c^pZdW§e;ZZa0cn±sBfe£uvsBc^t²0Zg\a0gJ¡Ùc^a0gµlg(e£Z9me^|Z|WsBuvsBc^t µsBu0a0g\fensBtI|9g\a
e;tI| sBtIqvg\a0uju0ZgaOg\fensBtI|9g\aqsBt9u0c§uOZgue£9mg^²cT&sBtIenmxm¬u0ZgqpZf s]q stIqg\a0u0g| st¬u0Zg2uJe;9mBg^{
µ9s]oO quvsxmma0g\ZaOgqvg\tuJqbu0ZggJ±Ie^oJubº;enmBpZgc;¡zu0Zg|9c^u0Za0cZ|9pIoJule;tI|fen(tZc;µ=Gg°e^|Z|9g| ¡Ùa0c^f
mBc;µu0c29sBd^ gJ± Gc^tZg\t9uquOccWZuensBt¤edWccZ|e;ZZa0cn±9sf)e;uvsBc^t²
´Ù¡ztZco\e;tIoJgJmxm]e;uvsBc^t)c o\oJpZaJqu0Zgt9pZfIg\abc;¡ze^|Z|WsBuvsBc^tIq*µsBu0a0g\fensBtI|9g\as]qbe;uf2cqvue;tI|
u0Zg#tpZfIg\ac;¡ue;9mBgg\tu0asgq*a0g\fensBtIqoJc^tIqvuJe;tun²´¡ro\e;tIoJgJmxm]e;uvsBc^t)c;¡f2c^a0guOIe;tu¸µc(|WsBd;sBuq
cZo\oJpZaqjsBt=e¤q¸stZd£mg§eW|Z|WsuscWt=µ9s]o0=o\e;t¬c^t9mBVIgu0Zgo\e^qvg^{³sx¡°u0ZggJ± Gc^tZg\tu)|WsMg\a0g\tIoJg
s]q^{&u0Zg)gJ± e^oJua0gqp9mu2o\e;t¬IgaOg\Za0gqvg\t9u0g|eWqe FIce;uvsBtZd7ÙGc;sBtutpZfIg\a2e;tI| u09pIqju0Zg
a0g\f)ensBtI|9g\aq2e;a0g2aZ²#g\tIoJgu0Zg2t9pZfIg\ac;¡/ue£9mg)g\t9u0avsBgq s¹q|9goJa0geWqvg|²~kle;tIoJgJmxm]e;uvsBc^t=c;¡
c^tZg|WsBd;sBu{Zc;µlg\ºWg\a{9fen§qvue;a0ue;te^|Z|WsBuvsBc^tZa0cZoJg|9pZa0gµ9s]o0a0pZtIq#u0Za0c^pZdWu0Zg(µZc£mg
ue£9mg^²
´StVu0Zg)o\e^qvgqc£¡lm]e;aOd^gwZmxm7Qst=µ#9s¹oO¬f2ge;tIq#m]e;a0d^ggJ± Gc^tZg\tu2|WsNMg\a0g\tIoJgqjc^tZg2c^aV\g\aOc
e^|Z|WsBuvsBc^tIq°¡¢aOc^f mBgJ¡¢u(qvp\oJg e£tI|§uO9s¹q Za0cZoJg|9pZa0goOmBge;avmB s]qqvpZIg\avsBc^aju0c)u0Zg2e^|n¸pIqu0f2g\t9u
c;¡q®sBd^tIq\²
g\9m]e^oJg\f2g\t9uc;¡ZIe^qvg§ 9ªeW|Z|WsuscWt=¡Ùa0c^f mBgJ¡¢u2uOc¤asdWu2aOg|9pIoJgqu0Zgt9pZfGg\a2c;¡
e^|Z|WsBuvsBc^tIq#sBt u0Zg(enº^g\ae;d^g^²9´®uqa0c^pZtI|WsBtZd)g\a0a0c^aGg\IeºWsBc^a#s¹qe;tIenmBV\g|)sBt¤qgoJuvsBc^t¤hZ²
' 2+-4.-op/ <+ 7j)5m8:9;j)+-,
0Zg#s]|9gejc;¡st9sBuvs]enmbe^|Z|WsBuvsBc^t2¡Ùa0c^f 9sBd^uOcmBc;µ?gJ±ZIc^tZg\t9uqo\e;t)IggJ± u0g\tI|9g|{Zqvcju0Ie;u~u0Zg
a0gJm]e;usºWgg\aOa0c^ac;¡bu0Zga0g\f)ensBt9stZduOg\a0fq|WsBfsBt9s]qvZgq\²&´Ù¡µg(oJc^f2ZpZu0gjpZtusmbu0Zg|WsMg\a0g\tIoJg
c;¡gJ±ZIcWtZg\tuq#Ig\uvµg\g\tVqvpZf e;tI|)wIaqu/ue£9mgjg\tuOa0)s]qI{Ie£t¤e;ZZa0cn±9sBfe;uvsBc^t c;¡u0ZgqpZf
µsBu0a0gJm]e;usºWg2g\a0a0c^a
s]q c^ZuensBtZg|{g\º^g\t sx¡lµg|Ws]q0o\e£a|Venmxma0g\fe[st9sBtZd g\tu0asgqÓ²C09s]q
¡Ùc;mxmBc[µqb¡Ùa0c^fu0Zg#¡Se^oJuu0Ie£uluOZg/ue£9mgg\t9u0avsBgqe;a0gc^a|9g\aOg|292gJ±ZIc^tZg\t9uq~µsBu0§e;u~f2cqvu
º;enmBpZgq#¡¢c^age^oO§gJ±ZIcWtZg\tu²wd^g\gqvgoJuvsBc^t§h¡¢c^a|9g\uensxm]q\²
_go\e£pIqvg e[mmu0Zg2a0g\f)ensBtI|9g\aqjIeºWguOc§IgsBtIqvg\a0u0g| sBtVu0Zg)ue;9mBge;tI| qvc^f2g2c£¡uOZg\f
Ienº^gu0cGga0goJc^tIq®s]|9g\a0g| ¡¢c^a9sBd^Zg\a/eWo\oJpZae^oJ^{Zu09s]qZaOc oJg|9pZa0g(qOeºWgqusfgc^t9mB2¡Ùc^aº^g\a0
mBc;µ e^o\oJpZaeWoJa0gy^p9sBa0g\fg\tuqÓ²
' W+=5 7j),78:9jL+-, lnjk9op*+-,7. /2131347546L8:9+-<
ZVgIg\a¡¢c^aOf+ZIe^qvg/e£tI|u0Zg\te^|Z|u0Zgue;9mBgg\tu0asgq*pIq®sBtZdemBc^tZde^o\oJpZfp9m]e;u0c^a²g\tIoJg
c^Zusf)enm e^o\oJpZaeWoJs]q&c^ZuensBtZg|{nu0Zgqvu0c^aJe;d^g&¡¢c^a&u0ZgsBt9wIt9suOgJmZa0goOs]qvg~a0gqvp9mBu&s¹q&fsBt9sBfsV\g|{
e;tI| e^o\oJpZfp9m]e;uvsBc^t§c£¡*q0o\e[m¹e£aZa0cZ|9pIoJuqoJc^tIq®s]qvustZd)c^pZuc£¡*qvg\ºWg\aenmIe;a0uqls¹q¡Se^oOsxmsBue£u0g|²
2 ~' 2 rz /¬1 -,./ 012
´®tu0Zg¡Ùc;mxmBc[µstZd ue;9mBg?µgV|9g\9s]oJu§¡Ùc^a)ge^oO enmBd^c^avsBu0ZfsBuq·fen±9sBfenme;tI| fsBt9sBfenm
gJ±ZgoJpZuvsBc^t¬uvsBf2g2f2ge^qpZa0g| sBt FIc9e;uvsBtZd7ÙIc£st9ueW|Z|WsuscWtIq({Üe£tI|¬kc^f2Ie£avs]qvc^tIqjk µ#Zg\a0g
u0Zgenº^g\ae;d^go\e^qvgµsmxmbIgoOmc9qvgu0c2u0Zgf st9sBfe[mruvsBf2gjº^g\a02c£¡¢u0g\t²
ZVg2e^q0qvpZf2gu0Ie£u°|9c^pZ9mBgmBg\tZd^uOVZa0cZ|9pIoJuqe;a0goJc^f2ZpZu0g|9u0Zg2qv9mxsBu0uvsBtZdf2g\u0ZcZ|
|9gq0oJasGg|·stqvgoJuvsBc^t§Z²(gJ±IoJg\Zu¡Ùc^au0ZgmBc^tZde^o\oJpZfp9m]e;u0cWalµ#Zg\a0gsBtu0g\dWg\a/e;avsBu0Zf2g\us¹o#s]q
pIqvg|² g\tIoJg stVenmxmc^uOZg\a(enmBd^c^avsBu0Zfqe)f st9sBfpZfgMc^aOu/c;¡Wt e£tI|Ve2f)en±sBfpZf c;¡;t
fp9mBuvsB9mxs¹o\e£uvsBc^tIq Ienº^gu0cIge^|Z|9g|uOcuOZg(ue;9mBgg\t9u0avsBgq\²
d^u0c^ae;dWgaOgy^p9sBa0g\f2g\t9uqe;a0g)qvu0c^a0g|·sBt¬u0Zg2m]e^quaOc[µq\²0 u0Zg2fen±9sBfenmxmBtZg\g|9g|
qvIeWoJg/|9pZavsBtZd(u0ZgoJc^fZpZue;uvsBc^t2|Ws]qva0g\de£a|WsBtZd(sBt9u0g\d^g\aqbe£tI|que^oO¶qvIe^oJg^² ´uOZglfg\f2c^a0
pIqvg| u0ca0g\Za0gqvg\t9u/uOZgsBt9wIt9sBu0gJmB¤ZaOgoOs¹qgaOgqvp9mBu²C0Zgº;enmBpZgqe;a0gd;sBº^g\t sBt§9sBuqµ#Zg\a0g
|9g\tZc^uOgqu0ZgtpZfIg\ac;¡9suJqpIqg|¡¢c^ae(FIce;uvsBtZd7ÙGc;sBtut9pZfGg\a/e;tI|g 9¥g\fen±7Ùg\fsBt N ^²
´Su2qvZc^p9m]| tZc^u(Gg§oJc^tIoJgenmBg|¬u0Ie;uc^t¬f2cZ|9g\a0t=oJc^f2ZpZu0g\aqÓ{sBtIe£a0uvs]oJp9m]e;a ´^dZk e£a 7
oO9sBu0goJu0pZa0gq\{*u0Zg2sBt9u0g\d^g\a2usfg qvZcWp9m¹|=eWoJu0pIenmxmBtZc^uGgtZg\d;mBgoJu0g|²JZVg¡¢pZaOu0Zg\a2|9c¤tZcWu
oJc^tIq¸s¹|9g\aq0o\enmxsBtZdgMc^aOuqsBt)u09s]qloJcWf2Ie;avs]qvc^tµ9s]o0e;a0gtZgoJgq0q0e;aO(¡Ùc^aenmxmzu0ZgenmBd^c^avsBu0Zf)q
µ9s]oOqvu0c^a0g u0Zg§aOgqvp9mBu§e^q2e º^goJu0c^a)c;¡FIce;ustZd7ÙIc;sBt9ut9pZfIg\aq\{*sS²g^²enmxmµsBu0Zc^pZu)u0Zg
mBc^tZd=e^o\oJpZfp9m]e;u0c^a²J0Zg§e[mdWc^avsBu0Zfq2e£a0g§|9g\tZc^u0g|¬9uOZgtpZfIg\aJq2c;¡u0ZgZa0goJg\g|WsBtZd
Ie;aJe;d^ae;ZIqlst µ9s]o0 u0Zg\)µlg\aOg(|9gq0oJavsBIg|²
Z²B ²© Z²
fen± tI` N 1v^;t
P
7S;t45S oJtmBc^d1St45k N £tZ
fsBt tI` N ;^tZ oJt)mcWd1St45k N ^tZ
0 ;g ;t ;t
´ ;g £g ;g
G²B I² I²
fen± 1¸;t N ^g 5® N ^g 1J;t N ;g 5S 1v;t N ;g 5S 1v;t7Ù^g 5S N ^g d
N
h;tk
N
h;tk
N
h£tk
N
h;tk
fsBt ^tZ
N
;tk WtZ
N
;tk ^tZ
N
;tk ^tZ
N
;tk N d
0 Wg ^g ^g ^g
´ Wg ^g ^g ;g
0e;9mBg3Gkc^fIe;avs]qvc^t9cWIg\ae;uscWt¤oJc^pZt9u/e;tI|qvuOc^ae;d^ga0gyWp9sBa0g\f2g\t9uq
mxmue;9mBgg\tu0asgq#e;a0gc^ZuJensBtZg|)oJcWpZtuvsBtZdu0Zgc^Ig\aJe;uvsBc^tIqe^q0qvpZf stZdu0Zg#¡Ùc;mxmc;µsBtZd
Za0cWIg\a0uvsBgq\²
TZc^au0ZgjmBc^tZde^o\oJpZfp9m¹e£u0c^a 1¸Z²¹ 5` |9g\tZc^u0gqe£te^|Z|WsBuvsBc^tVc;¡e)Za0cZ|9pIoJue;tI| d u0Ie;u
c;¡/e º[e[mpZg^{b u0Zg)gJ± uOae^oJuvsBc^tVc£¡uOZg2wItIenma0gqvp9mBu²b c^pZdW9m gqvuvsBfe;u0g| u0Zg2usfg2¡Ùc^a`
gyWpIenm]qu0Ie£u¡¢c^a N ²©; {u0Ie;u¡Ùc^a d9»^²;{e;tI|uOIe;u¡Ùc^a( 9+g +{ZpZu(uOZgqvg
wId^pZaOgq9sBd^9mB§|9g\Ig\tI| c^tuOZg(Ie;a|7e£tI|qvc;¡Ùu¸µe;aOg/c;¡u0ZgqvZqvu0g\f ²
°|Z|WsBuvsBc^tµsBu0a0g\f)ensBtI|9g\a/pIqvg| sBt 1¸Z²5re;tI| 1SI²B 5roJcqvuJq2e^|Z|WsBuvsBc^tIq\²
0Zgf)en±sBfe[mlIg\a¡¢c^aOfe;tIoJgc;¡1¸Z²5s]q2y^pIeW|9ae;uvs]o ¡¢c^a;t=qvpZf2fe;tI|ZqjµZg\aOge^qju0Zg
fsBt9sBfenms]qcWZuensBtZg|9 suOg\ae;uvsBc^tIqc£¡r^t§qpZf2fe;tI|Zq\²
0ZguvsBf2g¡Ùc^au0Zgc^aJ|9g\al9)gJ± Gc^tZg\tuenmBd^c^avsBu0Zf 1vZ²©5s]q|9c^fsBtIe;uOg|))u0Zg(qvc^aOuvsBtZd
uvsBf2g^²G fge;tIquOZg(qvIgoOsxwzoe^|Z|WsBuvsBc^t§µsuOmBc^tZd^g\af)e;tus¹qOq0eZ²
0Zgfen±9sf)enm/wZmxm7QsBt ¡¢cWa ¨c^ZGgJmBu ©q§e[mdWc^avsBu0Zf 1¸5js]q)c^ZuensBtZg| sBt¥Ie;u0Zc£mcWd;s]o\enmxm
oJc^tIqu0a0pZg|gJ±Ie;f29mBgq#c^t9mB^{Zu0Zgq0e;f2gZc;m]|Zq~¡Ùc^a1®I²©5²
°|Z|WsBuvsBc^t2µsuOaOg\fensBtI|9g\alo\e;tGg/oJc^f9sBtZg|µsBu02q®sBd^t2e^|nvpIqvu0f2g\t9uÜcWae^|Z|WsBuvsBc^t¡Ùa0c^f
mBgJ¡Ùu/u0cavsBd^9u{9sBtU1SI²B 5bu0Zgm]e;uOu0g\as]qmxs]qvu0g|²
0ZgfsBt9sBfenmÜgJ±ZgoJpZuvsBc^t§usfg¡Ùc^aenmxmrenmBd^c^avsBu0Zf)qpIq¸stZd)u0Zgm]e;a0dWgue;9mBgs]qc^ZuJensBtZg|{
sx¡lenmxmÜg\t9u0avsBgqe;a0g(e^|Z|9g||9pZavsBtZdZIe^qg2^²
´St21SI² 5{Jsx¡³;t Wgu0Zgfen±9sBfpZf uvsBf2g~s¹qcWZuensBtZg|{nsx¡zu0Zg~ue;9mBgs]q&wZmxmg|stZIe^qvg^{
Zg\tIoJg(ejfen±9sBfenmt9pZfGg\ac;¡re^|Z|WsBuvsBc^tIquOc(u0Zg#mBc^tZd2e^o\oJpZfp9m¹e£u0c^aIe^q~u0c(GgIg\av¡Ùc^a0fg|²
ue£9mg sBtIqvg\a0uvsBc^toJcqvuqGg\uvµlg\g\t§e;tI|h2oJc^f2Ie£avs]qvc^tIq#µsBu0 aZ²
2')\. ,&
ZVga0go\e[mmu0Ie;u-1LC
S D S EGJI)K
S
EG
B M
5|9g\tZc^u0gqu0Zg!FIce;ustZd7ÙIc;sBt9ulqvZqvu0g\f µsBu0Ie^qg\CV{ D
fe£tuvs]q0qOe|WsBd;sBuq\{;e;tI|gJ± Gc^tZg\t9uÜae£tZd^g EHGJILK
QQ EHG
B M
²0ZgbtZc^aOfenmxsVe;uvsBc^ts]qqvpIoOu0Ie;ub C
G ¡Ùc^age^o0 fe;t9uvs]q0q0e_G²G°qsBtu0ZgZa0g\º^sBc^pIqqgoJuvsBc^t
O
|9g\tZc^uOgq/e^|Z|WsBuvsBc^t µsBu0
a0cWpZtI|WstZd u0c§u0ZgtZge;a0gqvu(FIce;uvsBtZd7ÙGc;sBtu2t9pZfIg\a²
8
s]qju0Zg oJcWf2ZpZu0g|¬e;ZZa0cn±sBfe£uvsBc^t
u0c
8 ²
b½ I-gg\u
B ? 90G
?C
X -1LC
S D S EGJI)K
S
EG
B M 5 S
IK9 1 5 KµsuO
E
A E P N
E ? E ?O
A E ?
E
?O P S I
gg\u¡¢pZa0uOZg\a
8
90s
=?@ P B ? e;tI|
8
GgsBuqe;ZZa0cn±sBfe£u0g/º;enmBpZg(oJc^f2ZpZu0g|)92u0Zg#¡Ùc;mxmc;µsBtZd
enmBd^cWavsBu0Zf 3
8
3N9
B =
¡Ùc^aIc9 KJU=(|9c;µt9u0c2
8
3N9
8 O B ?
g\tI| ¡¢c^a
0Zg\t§u0ZgaOgJm¹e£uvsBº^g(g\a0aOc^a"c£¡Üu0ZgqpZf c;¡enmxm
B ?
s]qGc^pZtI|9g|
9
N
1
N
9 5 AP C A
µsBu0
h
C
C A
UV C C