Pointer Analysis: Haven’t We Solved This Problem Yet?
Michael Hind
IBM Watson Research Center
30 Saw Mill River Road
Hawthorne, New York 10532
[email protected]
ABSTRACT
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Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page. To copy otherwise, to
republish, to post on servers or to redistribute to lists, requires prior specific
permission and/or a fee.
PASTE’01, June 18-19, 2001, Snowbird, Utah, USA.
Copyright 2001 ACM 1-58113-413-4/01/0006 ... 5.00.
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REFERENCES
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NOoPTVU DRWS NO P DLKQ NX$YLZ[I\] F YÃ[ B T6d] Be ] Z H,c \[4g
T6d[^h*d G Y1YE] B hU GIB h FG h c \ij !*k$ 8t$Œ$t n;tIm‰s iq !*#wIr*r$Œ‰
om*E~L|7 ƒ 2/2 j !*#% q ) k$+ 84 j 42$3=2I+ 2$#+ # ƒ¬j 42$k$4!*3=8
>?# T{d[ eccC ] B h$\¥[4g `,bc7DLK"M NOoPTVU DRW³ •;ªµK [ B g c d c^Be^c [ B
T6d[^h*d G Y1YE] B hU GIB h FG h c¥¶Lc \^]yh B¾GIBC O4YLZ H,c Y cB`9G$` ]9[ B ij !*k$ 8
ŒI‹‰pon/Œ/or i IsonIp q #* NO PRTVU DRW©W [ ` ] ec \ Œ*t·£s$¸ iw„ !o:…Ir*r$l‰
IsI „ |!$8^€-#+ Ä !I+ 2$#;Š†!$84 % j 2$+ #‰ "!$#!$ :;84+ 8"Ž+ '%+ 4 + 2*#!*
!*884+ k*#3= #‰8^>?# T6d[ e^ccC ] B h*\¥[4g `fbcLD7K"M NO PT"U DRW³ ´/´
K [ B g c d c^Bec [ B T6d[h$d G Y1Y1] B h'U GIB h FG h cL¶7c \]fh B¾GIBC
O4YLZ H,c Y cB`9G$` ]?[ B iwj !$k* 8-Œ$s n/m$¯ i Ipon/t/ q #* NO PRTVU DRW©W [ ` ] e^c \
Œ*s·£s$¸ iq #t*‹*‹$‹;
I¯I „ |!$8 i ›)+ † + i„ ¢"!$Å #%4+ ^ i !*#% q 2*0?{89+ 3=!*+ #k7
+ 3 j !$<2*0u84 !$ !*† j 2*+ #‰ <!*#!* :;84+ 8-2*#2 j + 3=+ Æ !*+ 2*#w;>?#
N cÇ/cB`,b O Bw`?c d BG$` ]?[ BGIH N `?G$` ] eLDBGIH X$\^]f\=NX$YLZ[I\] F Y1iq :t*‹*‹;$
IlI7| ¢ 2$‰Ž i |7wR42 ‚‰ i !*#% ƒ ƒ !$37† 48^ ¢ !$89-+ #‰ j 42/ %4!$
!*848-!$#!$ :;84+ 8^>?#K [ B g c d c^Bec¥Âce [Id C [4g `fbc1@;ȉ`fbDLK"M
NOoPTVU DRWS NO P DLKQ NX$YLZ[I\] F YÃ[ B T6d] Be ] Z H,c \[4g
T6d[^h*d G Y1YE] B hU GIB h FG h c \ij !*k$ 8t$t$t n;t*Œ$¯ iq !*#wIr*r$p‰
IpIE| ;84w>#‰ j 42/ %4!$3=! :/Š£!$ + !*8!*#!* :;84+ 80,2$ j 2$+ #‰ 48 ›V:‰2*#%…ɉŠ£ + 3=+ + #k/># T6d [ ecc^C ] B h$\¥[4g `,bcD7K"M NO PRTVU DRW³ •IÊ
K [ B g c d c^Bec [ B T6d[h$d G Y1Y1] B h'U GIB h FG h cL¶7c \]fh B¾GIBC
O4YLZ H,c Y cB`9G$` ]?[ B iwj !$k* 8-t$ŒI‹In/t*m; i tI‹In/t*m q #* NOoPTVU DRW
W [ ` ] e^c \ t*r·£¯$¸ iq #LIr*r*m;
IrIE| ;84wv#% 43=+ #+ #k7 + 0,+ 3=!$#%!$ + !$84+ #k=2*0
%;:;#!*3=+ !$ :1!$ 2/ !* %'%!*!=+ #+ k* 9Š£2$4% V0,#+ 2$#!$
8 j + Ä !*+ 2*#8^>?#aK [ B g c d c^Be^c=Âce [Id C [4g `,bc N c^Ç;c^Bw`?ccB`,b
DBBFwGIHuD7K"M NX$YLZ[I\^] F Y_[ B T6d] Be ] Z Hfc \E[4g¥T6d[h$d G Y1Y1] B h
U GIB h FwG h c \^ij !$k* 8Ros$lonI¯*p iq !$#Ir$rI‹;
t*‹*E|+ ŽV!*# i ~L§ „ ~R+ # : i !*#% q <› „ 2$848^wž6: j Š†!$84 %
!* + !$8!$#!$ :;84+ 8^>?# T6d[ e^ccC ] B h*\¥[4g `fbcDLK"M NO PT"U DRW³ •/–
K [ B g c d c^Bec [ B T6d[h$d G Y1Y1] B h'U GIB h FG h cL¶7c \]fh B¾GIBC
O4YLZ H,c Y cB`9G$` ]?[ B iwj !$k* 8Ro‹$¯on$Il i olonIr q #* NOoPTVU DRW
W [ ` ] e^c \ Œ*Œ·£s$¸ iw„ !o:…Ir*r$p‰
t/ š |2* i„ <2/% i !$#% „ §;!$k$+ ‚ ƒ ^‡/+ #kL !$## 848"+ #' + #‡* %
+ 848^>?# N c^Ç/cB`,b O Bw`?c d BG$` ]?[ BGIH N `9G$` ] e7D-BGIH X*\^]f\=NX*Y¥Z[I\^] F Y1i
q #7tI‹$‹*‹;
t$tI „ {3=!$3=+ i R+ :$! i !$#%')u q ¡- #%4 #w ƒ 2*#‰./4Š£84 #84+ + ‚$
+ #‰ j 2/ %!* j 2*+ #‰89Š£21!$#!$ :;84+ 8<+ #' j 4 84 # 2I0u0,#+ 2$#
j 2*+ #‰ 48># T6d [ ecc^C ] B h$\¥[4g `,bc7DLKVM NO PRTVU DRW³ •IÊ
K [ B g c d c^Bec [ B T6d[h$d G Y1Y1] B h'U GIB h FG h cL¶7c \]fh B¾GIBC
O4YLZ H,c Y cB`9G$` ]?[ B iwj !$k* 8-t*m$ton/t$s$¯ i tI‹In/t*m q #* NOoPTVU DRW
W [ ` ] e^c \ t*r·£¯$¸ iq #LIr*r*m;
t$ŒI „ ¢"!$Å #%4+ ^ iq § ¢ 2*84 i § i !*#%-+ ‡$ #zJ!$9+ !$w2*# + #
:; R + 3=+ #!I+ 2$#E+ #+ # 84+ 2$# 2$#844!$+ #‰k*! j 8^>?#
T6d[ e^ccC ] B h*\¥[4g `fbcLD7K"M NO PRTVU DRW³ •/–°K [ B g c d c^Bec [ B
T6d[^h*d G Y1YE] B hU GIB h FG h c¥¶Lc \^]yh B¾GIBC O4YLZ H,c Y cB`9G$` ]9[ B ij !*k$ 8
p*son;r*¯ i Il nIr q #* NO PRTVU DRW¿W [ ` ] ec \ Œ*Œ·£s$¸ iw„ ! :‘or$r$p‰
t*m* „ ¢<!*Å #%+ ^ iq 2*0 i !$#% „ |!$8^w§ !* !$† 2*#‰./4Š£84 #84+ + ‚$RÁ2 Ž(!$#!$ :;84+ 884+ #k=+ #84!*#‰+ !*+ 2$# 2$#894!*+ #‰8
>?# T{d[ eccC ] B h$\¥[4g `,bc7DLK"M NOoPTVU DRW³ ´/´µK [ B g c d c^Be^c [ B
T6d[^h*d G Y1YE] B hU GIB h FG h c¥¶Lc \^]yh B¾GIBC O4YLZ H,c Y cB`9G$` ]9[ B ij !*k$ 8
t*s$Œon/t$¯*Œ i Ipon/t/ q #* NO PRTVU DRW©W [ ` ] ec \ Œ*s·£s$¸ iq #t*‹*‹$‹;
t$sI§ ¢ + #‡ i ~¥~R#2$† i !*#%¨7§!*‡o!*€-#+ Ä %'!$#!$ :;8+ 82*0u!$44! :
!*#%2*†;¤ "40, 4 # 8V+ #8942$#k$ :E?: j % !$#k$!$k* 8^>?# N c^Ç/cB`,b
O Bw`?c d BG$` ]?[ BGIH N `9G$` ] e¥D-BGIH X*\^]f\=NX*Y¥Z[I\^] F Y1iq #t*‹$‹*‹;
t$¯I q § ¢ 2$89 i„ ¢"!$Å #%4+ ^ i !*#%R+ ‡$ #zu2* :;3=2$ j + -‚$ 488
3=2*#2*3=2$ j + -Á2oŽ"Š£+ #84 #84+ + ‚‰ j 2$+ #‰89Š,2=!$#!$ :;84+ 8"0£2* ƒ w>#
N cÇ/cB`,b O Bw`?c d BG$` ]?[ BGIH N `9G$` ] e¥D-BGIH X*\^]f\=NX*Y¥Z[I\^] F Y1iq #
tI‹$‹$‹/
t$lIE+ :‰!/>#‰ j 42/ %4!$!* + !*8+ #k=+ # j 4 84 # 2I0u0,#+ 2*#
j 2*+ #‰ 48 ƒ -zV§'ž ^#+ !* „ 3=2=¯*t i„ o+ w€-#+ ‚$ 84+ : i | * i
or$r$t‰
t$pIE+ :‰!=!*#%)u q ¡- #%4 # ƒ 2$## + 2*#'!$#!$ :;8+ 8 j 4!$+ !*
+ #‰ j 2/ %!* ! j !*#!* :;84+ 8<0,2* ƒ O Bw`?c d BG$` ]?[ BGIH<Ë [ F d BGIH [4g
T G d GIHfH,c^H T6d[^h*d G YEY1] B h*i t*m·£¯$¸ s*m$lon/s$l$p i Ir$r*¯/
t$rIE+ :‰!=!*#%)u q ¡- #%4 #>?8-+ -!= i !=|< i 2$<!E:; + k*! j ̅¼8! j !*#!* :;84+ 80,2$< ! j Š£%+ 4 % j 2*+ #‰ 48<+ # ƒ >?#
K [ B g c d c^Bec¥Âce [Id C [4g `fbc1@;Í d C1DLKVM NO PRTVU DRWS NO P DLKRQ
NX$YLZ[I\] F YÃ[ B T6d] Be ] Z H,c \[4g¥T6d [h*d G Y1Y1] B hU GIB h FwG h c \^ij !$k* 8
^nIs iwq !$#or$r*¯/
Œ*‹*E+ :‰!=!*#%)u q ¡- #%4 #z{;+ #k j 2*+ #‰ <!*#!* :;84+ 8<2¥ŽV2*‡
>?#°@;ȉ`,bD-BBFwGIH6DLK"M NO P DLKRQ6S NO PRTVU DRW NX$YLZ[I\^] F YÃ[ B
`fbc T6d] Be ] Z H,c \[4gLT6d [h*d G Y1Y1] B hU GIB h FwG h c \^ij !$k* 8Rot/nIŒ*Œ i
q !*#wor$r$p‰
Œ/ E+ :‰! i |7)! ‚‰ 9?: i !$#%|7§; ^v#'R+ 3 j 2$9!$# 2*0
j 2*+ #‰89Š£21!$#!$ :;84+ 8<!$#%2* <3= 3=2*9:%+ 84!$37†+ k$!*+ 2$#3=2/%8
0,2$ ƒÎj 42*k$4!$3=8^>?# T6d[ e^ccC ] B h*\¥[4g `fbcLD7K"M NO PT"U DRW³ ´/”
K [ B g c d c^Bec [ B T{d[h$d G Y1Y1] B hU GIB h FwG h cL¶7c \^]yh B¾GIBC
4O YLZ H,c Y cB`9G$` ]9[ B i t*‹In/t$t q #*ž2=! jj !*
Œ$to'¡-!$89+!$#%…§¡-2*9Ž+ Æ*€-84+ #k=89!I+ 784+ #k$ 7!*884+ k*#3= #‰"0,2$43
2=+ 3 j 42 ‚‰Á2 Ž"Š+ #84 #84+ + ‚$ j 2$+ #‰ "!$#!$ :;84+ 8^>?# T6d[ e^ccC ] B h*\L[4g
`fbcDLK"M NO PT"U DRW³ •/–AK [ B g c d c^Bec [ B T{d[h$d G Y1Y1] B h
U GIB h FwG h cL¶Lc \^]yh B¾GIBC O4YLZ H,c Y cB`9G$` ]9[ B ij !*k$ 8-r*lono‹‰s i
olonIr q #* NO PRTVU DRW©W [ ` ] ec \ Œ$Œ;·£s$¸ i„ !o:…Ir*r$p‰
Œ$Œo š ¡ + #‰Æ !$#%…v7ž!$4%+ | 3=!$#%Š£%4+ ‚$ # j 2$+ #‰ "!$#!$ :;84+ 8^
># T6d [ ecc^C ] B h$\L[4g `,bcD7K"M NO PRTVU DRW³ ´/”µK [ B g c d cBec [ B
T6d[h$d G Y1Y1] B hU GIB h FG h cL¶7c \]yh BGIBC O4Y¥Z Hfc Y c^Bw`?G$` ]?[ B i
tI‹In/t$t q #*ž21! jj !$^
Œ*mI š ¡ + #‰Æ !$#%…v7ž!$4%+ €- 4!*Š,0£!*89!$ + !$84+ #k=!$#!$ :;84+ 8<84+ #k
ƒ ) 3=+ + 2*# + # 8<2*0 ƒ 2/%R+ #'!184 2$#%>?# T6d[ ec^cC ] B h*\=[4g
`fbcDLK"M NO PT"U DRW³ ´/”°K [ B g c d c^Bec [ B T{d[h$d G Y1Y1] B h
U GIB h FwG h cL¶Lc \^]yh B¾GIBC O4YLZ H,c Y cB`9G$` ]9[ B i t*‹In/t$t q #*ž2
! jj !$^
Œ$so')u q ¡- #%4 # iq ¡-3=3= i !*#%R š + 2$ !*w†894!$+ 2$#8<0,2*
4 48+ ‚‰ j 2*+ #‰ <%!*!=894 8 >?3 j 42 ‚;+ #k¥R!$#!$ :;8+ 8-2*0
+ 3 j 4!*+ ‚‰ j 42$k*!*3=8^>?# T6d[ ec^cC ] B h*\=[4g `fbcLD7K"M
NO PRTVU DRW³ •‰@AK [ B g c d cBec [ B T6d[^h*d G YEY1] B hU GIB h FwG h cL¶Lc \^]yh B
GIBC O4Y¥Z Hfc Y c^Bw`?G$` ]?[ B ij !*k$ 8t*m‰r n;t*¯*‹ i olonor q #* NO PT"U DRW
W [ ` ] ec \ t$l·£l*¸ iq :Ir*r$t/
Œ$¯o')u q ¡- #%4 #E!$#% š + 2* !$zu!*4!$ + Æ + #k j 2*k$4!$3=8"Ž+ 4 48+ ‚‰%!*!=8944 8^ O ™"™V™©Q d GIB \ G/eo` ]?[ B \[ B T G d GIHfH,c^H{GIBC
¶ ]f\ ` d]?º F`9c^C NX$\ `9c Y1\^i /·?I¸ Œ*son‰m‰l iq !*#wIr*r*‹/
Œ$lo ¢ ¡- #k$ + #ž6: j R+ #;0, 4 # "Ž+ j 2$ :;3=2* j + -4 484+ 2*#wD7K"M
Q d GIB \ G/e ` ]?[ B \1[ B T6d[^h*d G YEY1] B hU GIB h FwG h c \ GIBC NX$\ `?c Y1\i
os·£t$¸ t*s$Œ n;t$p*r i j ^or$r*Œ/
Œ$po „ ¡+ #% i„ ›V4‡$ i zJ ƒ !$4+ #+ i !$#% q Š£|7 ƒ 2$+f>#‰ j 42/ %4!$
j 2$+ #‰ "!$ + !*8!*#!* :;84+ 8^D7K"MŸQ d GIB \ G/eo` ]9[ B \[ B T6d[h$d G Y1Y1] B h
U GIB h FwG h c \ GIBC NX$\ `?c Y1\i t‰/·,m‰¸ pIm‰p n;p$rIm iq :‘or$r*r/
Œ$ro „ ¡+ #%'!$#%z{+ 2$ +,-8484 884+ #k=Rw 82I0uÁ2oŽ"Š£8 #84+ + ‚;+ ?:
2*# j 2*+ #‰ <!* + !$8<!$#!$ :;84 8^>?#…7)‚;+ i %+ 2* iU c^eo`fF d cRW [ `?c \7] B
K [IY¥Z F`9c dN e ] c^Be^co¦<”‰È;´‰Í ij !*k$ 8s$lon/p/*§ j 4+ #k$ 9Š,¨{ 4 !$k i Ir*r$p‰
z{42/ %+ #k$860,42$3©1ȉ`,b O Bw`?c d BG$` ]?[ BGIH N `9G$` ] e7D-BGIH X*\^]f\
NX$YLZ[I\^] F Y m$‹I „ ¡+ #%'!$#%z{+ 2$ +,&¬+ j 2*+ #‰ <!*#!* :;84+ 8-842* %'>"84oÌ>?#
O B`9c d BG$` ]9[ BGIH NX*Y¥Z[I\^] F Y—[ B N[4g `f˜G d c…Qc \ ` ] B h GIBCED-BGIH X$\],\i
k/t*‹$‹*‹;
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Œ*r·?I¸ Œ‰n/s$s iq !*#wtI‹$‹;*
m‰to§¡-2*4Ž<+ Æ*z{4 + 84RÁ2 Ž<Š£+ #8 #84+ + ‚‰R3=! :/Š£!$ + !*8-!$#!$ :;8+ 8+ 8
š z6Š¡-!*4%wD7K"MŸQ d GIB \ G/e ` ]?[ B \[ B T6d[^h*d G Y1YE] B hU GIB h FG h c \
GIBC NX*\ `9c Y1\^i Ir;·9o¸ n/¯ iq !$#Ir*r$l/
m‰Œo§¡-2*4Ž<+ Æ i zJz60£ + w i !$#%ž-&( j 8| j #% # !$#!$ :;84+ 8
0,2* j 2*+ #‰ "‚I!$4+ !*† 8># T6d [ ecc^C ] B h$\¥[4g `,bc7DLKVM
NO PRTVU DRW³ –/•°K [ B g c d cBec [ B T6d[^h*d G YEY1] B hU GIB h FwG h cL¶Lc \^]yh B
GIBC O4Y¥Z Hfc Y c^Bw`?G$` ]?[ B ij !*k$ 8t$pon‰m$‹ i t‰n/t$Œ q #* NOoPTVU DRW
W [ ` ] ec \ t*m·£l*¸ iq :Ir*p$r/
m$mI'zJ¡%!$‡}84 3=!$#‰+ R3=2/% w2I0640, 4 # - 2*#‰+ #k¥!*#%+ 8
!*†894!$+ 2*#w>?#aK [ B g c d c^Be^c=Âce [Id C [4g `,bcE”‰•/–;½1DLK"M
NX$YLZ[I\^] F Y—[4g¥UO4NT GIBC “ FBe ` ]?[ BGIH T6d[^h*d G Y1YE] B h$ij !$k* 8
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m‰so q ¡3=3= i )6 q ¡- #% # i !*#%R š + 2$ !*w†894!$
% 84 4+ j + 2*#2I0 j 2*+ #‰ <%!*!=894 8 -#! jj 42$!$'0,2$
+ 3 j 42 ‚;+ #kLR!$#!$ :;8+ 8!$#%2 j + 3=+ Æ !I+ 2$#2*06+ 3 j 4!*+ ‚‰
j 42$k*!*3=8^DLK"M U c ``9c d\=[ B T6d[^h*d G Y1YE] B hU GIB h FG h c \ GIBC
NX$\ `9c YE\i /·£Œ$¸ tIm‰Œon/t$¯I‹ i § j wIr$r*t/
m‰¯o§>?84‰+ ! !$#%'zJ&(wv ¡ !$4#w›V>"!$8-!*#!$8484 9+ 2$# !$#k$!$k$0,2$
37!*† %!*!1894 8^>?#°@;–‰`,b…D-BBFwGIHuDLK"M
NO P DLKRQ6S NO PRTVU DRW NX$YLZ[I\^] F Y_[ Ba`,bc T6d] Be ] Z Hfc \E[4g
T6d[h$d G Y1Y1] B hU GIB h FG h c \^iq !*#wtI‹$‹;*
m‰lo š |7 q 2*# 8<!$#%…§§ „ ^#+ ‡ ¢ 2oŽ¼!*#!* :;84+ 8!*#%
2 j + 3=+ Æ !*+ 2$#E2*0u)>9§z6Š£ + ‡*R8444 8^>?#…§w§ „ #+ ‡=!$#%
š |7 q 2*# 8 i %+ 2$48 iT{d[h$d G Y “ H [ ˜(D-BGIH X$\]f\ QJbc [Id^X GIBC
D Z/Z H ] eG$` ]?[ B \i ! j "m ij !$k$ 8o‹$tonoŒ/*wz{4 #‰+ Š£¡-!$ i Ir*p/$
m‰po&()!$#%+, O B`9c dZd[ ec^CIF d GIHwD-H ] G \] B h…] Ba`fbc T6d c \ c^Bec [4g
T<[I] Bw`?c d^\ z{|( 84+ 8 i ;k$ 48€#+ ‚$ 48+ ?: i Ir*r$t/
) ƒ §"Šž"<Š9IlIm;
m‰ro&()!$#%+,€#% + %!$†+ + ?:¥2*0689!*+ !$#!$ :;8+ 8DLKVM U co`£`9c d\1[ B
T6d[h$d G Y1Y1] B hU GIB h FG h c \ GIBC NX$\ `9c Y1\^i /·,m‰¸ Œ*t$Œ n;Œ$Œ*l i | *
or$r*t/
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!$8484+ Ä !I+ 2$#>?#a”‰–‰`fbD-BBFGIH6D7K"M NX*YLZ[I\] F YÃ[ Ba`fbc
T6d] Be ] Z H,c \E[4g¥T6d[^h*d G YEY1] B hU GIB h FwG h c \ij !*k$ 8-r*Œono‹‰p iwq !$#
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+ #‰ j 42/ %4!$ j 2$+ #‰ "!$ + !*84+ #k/>?# T6d[ ec^cC ] B h*\L[4g `fbc7D7K"M
NO PRTVU DRW³ •‰@AK [ B g c d cBec [ B T6d[^h*d G YEY1] B hU GIB h FwG h cL¶Lc \^]yh B
GIBC O4YLZ H,c Y cB`9G$` ]9[ B ij !*k$ 8-t*Œ$s n;t*m$p i Il nIr q #* NO PRTVU DRW
W [ ` ] e^c \ t*l·£l$¸ iq :…or$r*t/
s$tI1&()!*#%+ i ›L<:;% i !$#%…§w!$#k;>?#‰ j 2/ %!*84+ %
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D7K"M NO PRTVU DRW³ •/Í°K [ B g c d cBec [ B T6d[^h*d G Y1YE] B hU GIB h FG h c
¶7c \^]yh B¾GIBC O4YLZ H,c Y c^Bw`?G$` ]?[ B ij !$k$ 8s$¯ n;¯$l i t$Œon/t$s q #*
NOoPTVU DRW©W [ ` ] ec \ t$p;·¯*¸ iq #LIr$r*Œ/
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894R!* 884 8^>?# T6d[ eccC ] B h*\¥[4g `,bc7DLK"M NO PT"U DRW³ –/–
K [ B g c d c^Bec [ B T6d[h$d G Y1Y1] B h'U GIB h FG h cL¶7c \]fh B¾GIBC
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t*Œ·£l$¸ iq :…or$p*p/
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O Bw`?c d BG$` ]?[ BGIH NX$YLZ[I\^] F Y_[ B N[4g `,˜G d c…Qc \ ` ] B h GIBC1DBGIH X$\^]f\i
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[ B T6d[h$d G Y DBGIH X*\^]f\-g [Id¥N[4g `f˜G d c‘Q [I[ H \ GIBC'™6B h*] Bcc d] B h*i
q #7tI‹$‹/$
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W [ ` ] e^c \i t*p·£r$¸ ¯*lon/l*‹ i §; j wIr*r$Œ‰
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N c Y GIB` ] e \ S G \ cC T6d[^h*d G Y M°GIB ] Z FHfG$` ]?[ B iwq #LIr*r$s‰
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GIBC N[4g `,˜G d c…Qce^b/B [ H [^h*X$i m*‹·?$^nIt*¸ l*‹/n;l*t$¯ iwš 2 ‚Ir*r$p/
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NO PRTVU DRW³ ´/´µK [ B g c d cBec [ B T6d[^h*d G YEY1] B hU GIB h FwG h cL¶Lc \^]yh B
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D Z/Z H ] eG$` ]?[ B \i vt*‹*‹;$
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“[ FBC/G$` ]?[ B \[4g7N[4g `f˜G d c=™6B h*] Bcc d] B h p*‹I'<<0? ƒ 2$#‰./4Š+ #84 #84+ + ‚$R!$ + !*8!*#!* :;84+ 8-4 2$#84+ % 4 %;>?#
T6d[ eccC ] B h*\L[4g `,bcDLK"M NOoPTVU DRW³ •/È°K [ B g c d c^Be^c [ B
T6d[h$d G Y1Y1] B hU GIB h FG h cL¶7c \]yh BGIBC O4Y¥Z Hfc Y c^Bw`?G$` ]?[ B ij !*k$ 8
oŒon/t$t i opon;t‰ q #* NO PT"U DRW©W [ ` ] ec \ Œ*‹·£¯*¸ iq #¥or$r*s/
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T6d[ eccC ] B h*\L[4g `,bcDLK"M NOoPTVU DRW³ ´/´µK [ B g c d c^Be^c [ B
T6d[h$d G Y1Y1] B hU GIB h FG h cL¶7c \]yh BGIBC O4Y¥Z Hfc Y c^Bw`?G$` ]?[ B ij !*k$ 8
tI‹‰p n;t/op i Ip n;t‰ q #* NO PRTVU DRW5W [ ` ] ec \ Œ*s·£s$¸ iq #tI‹$‹$‹/
p$to'<<0?zu!*9+ + 2$#+ #kL%!I!IÁ2 Ž(!*#!* :;84 88+ #k¥?: j 8>?#
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NX$YLZ[I\^] F Y—[ B T{d^] Be ] Z Hfc \1[4g=T6d[^h*d G Y1YE] B hU GIB h FG h c \ij !*k$ 8
oson/t$¯ iq !*#wor$r$l‰
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j !$k* 8-t*p$son/t$r*Πiq !$#Ir*p$p/
p*mI'k$+ #!=!$#% „ ƒ w<+ #!*4%wzu2*+ #‰ <!*#!* :;84+ 8<0,2*
37 + 4 !$% % j 42$k*4!$3=8^>?# T6d[ ec^cC ] B h*\L[4g `fbc7D7K"M
NO PRTVU DRW³ •/•°K [ B g c d cBec [ B T6d[^h*d G YEY1] B hU GIB h FwG h cL¶Lc \^]yh B
GIBC O4Y¥Z Hfc Y c^Bw`?G$` ]?[ B ij !*k$ 8l$lon/r*‹ i ^n/m „ ! :$ NO PRTVU DRW
W [ ` ] ec \ Œ*m·£s*¸ iw„ ! :‘or$r*r/
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j 2$+ #‰ 48 i !$44!o:+ #%+ 8 i !*#%!$ 8484 %'3= 3=2*4:E4 k$+ 2$#8>?#
T6d[ eccC ] B h*\L[4g `,bcDLK"M NOoPTVU DRW³ ´/´µK [ B g c d c^Be^c [ B
T6d[h$d G Y1Y1] B hU GIB h FG h cL¶7c \]yh BGIBC O4Y¥Z Hfc Y c^Bw`?G$` ]?[ B ij !*k$ 8
op$t nIr*s i Ip n;t‰ q #* NO PRTVU DRW5W [ ` ] ec \ Œ*s·£s$¸ iq #tI‹$‹$‹/
p$¯o'›7w":;% i &()!*#%+ i zJ§/2/‡/8 i §!*#k i !$#%
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[ B T6d [h*d G Y1Y1] B hU GIB h FwG h c \ GIBC NX*\ `?c Y1\^i t$Œ;·£t$¸ i„ !$^t*‹$‹/$
p$lo „ §;!$k*+ ‚ i ž j 8 i !$#%'R& + 3§;2$ ‚;+ #k¥84! j Š£!$#!$ :;84+ 8
j 42$† 3=8V+ # !*#k*!*k$ 8"Ž+ % 89+ ‚‰ j %!*+ #k;>?#°@;Í d C
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T6d] Be ] Z H,c \E[4g¥T6d[^h*d G YEY1] B hU GIB h FwG h c \ij !*k$ 8Ro¯on/Œ/ iq !*#w
or$r*¯/
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j 42$† 3=8V+ # !*#k*!*k$ 8"Ž+ % 89+ ‚‰ j %!*+ #k;D7K"M
Q d GIB \ G/e ` ]?[ B \1[ B T6d[^h*d G YEY1] B hU GIB h FwG h c \ GIBC NX$\ `?c Y1\i
tI‹·?I¸ ^n;sI‹ iq !$#Ir*r$p/
p$ro „ §!*k$+ ‚ i ž- j 8 i !$#%'R& + 3/zu!$4!*3=4+ 84! j !*#!* :;84+ 8
‚;+ !1ŒIŠ,‚*!* % 2$k*+ *>?#A@½$`fbD-BBFwGIHuDLK"M NOoP DLKQuS NO PRTVU DRW
NX$YLZ[I\^] F Y—[ Ba`,bc T6d] Be ] Z Hfc \E[4g¥T6d[h$d G Y1Y1] B h'U GIB h FG h c \i
q !$#wIr$r*r/
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j 2$+ #‰ V!$#!$ :;84+ 8^>?#zJ;¨7¡- #‰ #9:;^‡ i %+ 2$ iU ce `,F d cW [ `?c \] B
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z{42/ %+ #k$860,42$3©7Ê`,b O Bw`?c d BG$` ]?[ BGIH N `9G$` ] e7D-BGIH X*\^]f\
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NX$YLZ[I\] F YÃ[ Ba`fbc T6d] Be ] Z H,c \[4gLT6d[^h*d G YEY1] B hU GIB h FwG h c \i
j !$k* 8Rnom iwq !*#wor$r$l‰
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