HAL Id: inria-00074387
https://hal.inria.fr/inria-00074387
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
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
A Component model for synchronous VLSI system design
Dominique Lavenier, Roderick Mcconnell
To cite this version:
Dominique Lavenier, Roderick Mcconnell. A Component model for synchronous VLSI system design.
[Research Report] RR-2285, INRIA. 1994. �inria-00074387�
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE
! "$#&%(')*(#+, - #/.10
Dominique Lavenier, Roderick McConnell
N˚ 2285
mai 1994
PROGRAMME 1
Architectures parall`eles,
bases de donn´ees,
r´eseaux et syst`emes distribu´es
! "$# %(') * #+, - # . 0
! "$#%&('*)+&-,./0/"121
3$465(7(498;:<:.=?>A@ BA4DCDEFHGI=%C2G6J4I=LKMN8%4D8;OHOP=QOH=%K2RTSN8UKV=%KXW=YW5UZZ\[=Q=%K]R4[=%K=%8;J^<=QGXKV_KVG`P=Q:<=%KWFaKGI46FbSJc[=LK
3$4I5(d=`GXB3e
fX8;MM-5U4IGgW=h4I=%CDE=Q49CiE=AZkjml(l(nUop@ :q8%F$>QrUr;s?@ l(t?MN8;7U=%K
u<vw2x%y%z{(xT| }=~M4I=LKV=QZG"8:.5W=QOA5U4~8ObFHS4D8%4I_5;pKV_ZNCDE4I5UZ5(JNKq he<C]5(:<MN5(Z=QZG9K2RX\EFaCDE
W=%K6C24IFHSN=%K$S-5UGIEqGIE=QFb4$JZNC]GIFb5UZq8;ZWGIE=`Fb4GIFH:<FbZ7WFa8%7(4D8%:qK2R\FbG6E5(JGcW=%K6C24IFHSFbZ7hG6E=FbZGI=`4IZN8%OFb:<
MOH=Q:<=QZGD8%GIFb5UZk5%GIE=gC2Fb49C2JFHGQXJ4:<5W=QOFaKSN8(K=%W5UZT_ZNCiE4I5(Z5(JNK8;G98kOH5;hRT\FHGIE<=Q^GI=`ZG6Fb5(ZK
GI5q:<5W=QO eAC]Fb4DC]JFbG9K2R8;ZNW~GI5<T=`4IF_qG6EN8;GY8<K_KGI=Q:W=%KVFH7(Z=LW\FbGIE~ eAC]5(:<MN5(Z=QZG9K4I5U:
5(J4\ObFbS4D8;46_?FaK!M465(MN=Q46Ob_.KV_ZNCiE4I5(ZFbQ=%W$e0ZFbG6Fa8%ObFbL8;GIFH5(Z8%ZNW<GI=Q46:<FbZN8%GIFH5(Z.C25(ZNWFbGIFH5(ZNK8;46==`^MOHFaC2FHGIOH_
CDE=%CDT=%W
TIY Ny%¡wU|¢WFb7UFbGD8%OKVFH7(ZN8%OM4I5C2=LKIKVFHZ7RKVMN=%C]Fa8;OHFbQ=LW<KV_KVG6=Q:qK!W=%KVFH7(ZR hme
£¥¤§¦
¨0©ªQ«
¦
¨!¬b©®¯i°
±²h³i´%´%µ¶V·`¸¹³iº¶6»A·]¶Vµ¼¸¾½2²g¿¸¾À¾À(´U¶Á;µ¶¼Â¶²Qº¶6»k³DºÃÄ%ÅÆÇDÈ
ÉVÊË
¸¾¼X¿½]µÂÌ<¿Í³i¼XÁU³iµº¸¹³iÀÎÀ¾ÏpÐHÑ%²U»Q¶I»<´QÏ.º
Ë
¶?Ò%µÂ¶²UÓ ËÕÔ
½Q½2µ»Q¸¾²U³iº¶6»qÃÖ¶¼¶I³DµÓ
Ë
ŵ½2×]µ0³DØ+±ÚÙÛܽiк
Ë
¶?Ò%µÂ¶²UÓ
Ë
Û¸¾²%¸¾¼ºÂµÏ$½DÐTö¼Â¶6³Dµ0Ó
Ë
³D²(»ÄQÁU³2Ó0¶]ÝD´QÏ$º
Ë
¶Þ¼ÂÁ%µ¸¾ºNßÃÖ±Á%µÂ½6à0¶6ÓºÙ½$á]á]â2ãÙ±$Ù±Æã%ÝD³i²U»$´QÏ$º
Ë
¶ä½LÓº½]µ0³DÀåÆÓ³D²U»L¸æ»;³Dº¶
Ù¶Vºa¿½2µÌ\Ðb½]µÄQÏQ¼ºÂ¶Ø³D²U»Ûh³2Ó
Ë
¸Î²;¶Ú±µÓ
Ë
¸¾º¶IÓ0ºÑ%µÂ¶½iк
Ë
¶ä$ÃÞNä!ç
ÉÉiè
ä½2ØX¸¾²%¸¹é2Ñ%¶]çëê³V·]¶²;¸Î¶Vµì
è
ýQ»Q¶µ¸¹ÓÂÌTçëÛhÓ
Ô
½]²;²%¶À¾Àbì9í¸¾µ¸¾¼³;çйµ
Unit´e de recherche INRIA Rennes
IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France)
T´el´ephone : (33) 99 84 71 00 – T´el´ecopie : (33) 99 84 71 71
# #+!#, # % ') * #+! #
w*| A5UJNKpM4[=%K=QZG65(ZNK?JZ¢:<5WP=`Ob=qW="SFbSObFb5UGIEÍP=mJ= W="C25(:<MN5 KI8;ZGDK? heYKV_ZNCDE4I5UZ=%K
Mc[=Q46Fb5WFmJ=%KmJFNM4[=%C2FKV=§P8Oa8A5UFaKOH=5UZNC2G6Fb5(ZZ=Q:<=QZG=QG!O¾8(KMN=%C2GGI=Q:.M-5U4I=QOW=%K!C]5(:<MN5TK68;ZGDK]RK68;ZNK
W[=QG98;FHObOb=`4$Oa8h4[=%8%ObFaK68;G6Fb5(Z.FbZGI=Q46Z=T=%C]F-MN=Q46:<=QGW=hK¾8UKIKVJ4I=Q4mJJZ.KICDE\[=Q:q8hW=%K6KVFHZ\[=?P8kO¾8%FaW=XW=C2=%K
C25U:<MN5TKI8%ZG9K=%KG\SFb=`Z<K_ZNCDE465(ZFK[=T=%K!C25UZNWFHGIFb5UZNK\WFbZFHGIFa8%ObFKI8;G6Fb5UZ=QGcW=G6=Q4I:<FHZN8;FKV5UZ<K5(ZG\8;JKIKVF
C25UZNKVFW![=Q4[=`=%K2A5UJNKkFbZGI465WJFaK5(ZNKkJZ=<SN5HGI=Q9P8;5(JG6FbO KkOb5(7UFaC2FH=QObOH=kMN5(J4M4[=%C2FKV=Q4hOb=LKE5(4IOH5(7U=%K2R$MJFaK
Z5UJNK!Ob=%K8%MMObFmJ5(ZNKhP8hOå=`Oa8;SN5U4D8;G6Fb5UZqW=%K:<5WP=QOH=%K$f\ P8MN8%4IG6Fb4\W=%K:<5WP=QOb=%KC25U:<MN5(46GI=Q:<=`ZG98;OaK]
x%w2D{"!~| C]5(ZNC2=`MGIFH5(Z"W=YKV_KVG`P=Q:<=%KKVMc[=%C]Fa8;OHFaK[=%K2RT heDRG64D8;FHGI=Q:.=QZGWFH7(FHGD8;OÍW=YKVFH7(ZN8%J^
4
*,+$" .
!E=XGI498;ZNKFbGIFH5(Z<SN=QG=Q=QZ.8SN=QEN8QFb5(498;ON:<5W=`O5;Ú8YKV_KVGI=`: 8;ZNW<8hf\=Q7(FKVG6=Q4 Ö498;ZNK0=Q4\=QT=`O650f\(7
:<5W=`O\FaK5%GI=QZ*8WF98 C2JObGKGI=QMÍRFHZT5UObFbZ78¢C25U:<MOb=`GI=<46=QÂ\46FbG6=5;Y=%8UCiE C25(:.M-5UZ=QZGQe0Z GIEFaK
8;46GIFC2Ob=h!=hM465(MN5TK=8<KV_KVG6=Q:q8%GIFaCg8;MM465T8UCiE"GI5.W=QT=QOH5(MFHZ78;Zf!Ob=`T=QOK_KGI=Q: :.5W=QO0RKVG98;4IG6FbZ7
4I5U:+GIE=gS-=`EN8QFH5(4D8%ONOb=QT=QO!E=8%MM4I5 8(CDEqFaK$SN8(K=%W5UZq8pT_ZNCDE4I5UZ5(JK!8%GD8kOb5%:5;7 W=%KVFH7(Z
:<=QG6E5W5UOb5(7U_ 5U4GI498;ZNKFbGIFH5(ZFHZ7<SN=QG!=`=QZ~8<SN=QEN8QFb5(498;O$:.5W=QO8;ZW K_ZNCDE465(Z5UJNK heXC2Fb49C2JFbG9K2
}=?C25UZNKVFW=Q4X8;Zf \KVFH:JO8;G6Fb5(Z C25(:<MN5UZ=QZGAG65SN=?C]5(:<MN5TK=%W 5%G!5.KVJSÂ=QOH=Q:<=QZGDK<508UKAKE5%\Z
SN=QOb5%=7?>8GIFb:.FbZ7Õ8(KVMN=%C]G?\EFaCDE W=QGI=`4I:<FHZ=%KGIE=.:<5(:<=`ZG9K8%G\EFaCDEGIE=qFHZMJG9K?8;ZNW¢5(JG6MJGDK
=Q^FaKG*@$8%ZNW¢8;Z 5(MN=Q4D8%GIFH5(ZN8%O8UKVMN=%C2G?\EF CiE¢MN=Q45(4I: KGIE=8UC2GIJ8;OXCQ8%OaC2JO8;G6Fb5(ZÍRF0=TG6E=<SN=QEN8QFb5U4Q
}=E8LT=CiE5 KV=QZqG6EFaK\C25U:<MN5TKFbGIFH5(ZqSN=%CQ8%JNKV=hFbG\MN=Q46:<FbG9K$JNKG65?M4I=LKV=Q46T=GIE=hSN=QEN8QFb5U4D8;O8UKVMN=%C2GX5;
C25U:<MN5(Z=QZGDK]R\EFbOH=Y8(WWFHZ7<G6E=hZ=%C2=%K6KI8%4I_qGIFH:<FbZ7h5(4hf \KVFH:JO8;G6Fb5(ZÍe0Z5U4DW=Q4XGI5.W=QT=`Ob5(M"8%Z
f\:<5W=QO0R(=A46= TJFb46=XW=QGD8%FbOH=%WkGIFH:<FbZ7gFbZ5U4I:q8%GIFb5UZk5(4GIE=X he$C]Fb4DC]JFbG9KA5KVJNCDE.8(KG6EN8;G7(FHT=QZ
5(ZÕ8W8;GD8UKVE=`=QGB7\SJG\Z5(GgGIE=YKVMN=%C]F9CCQK!5%GIE=kFbZGI=`4IZN8%OFb:.MOb=Q:.=2ZGD8%GIFb5UZRT:q8;FbZ7kFbG\M4D8(C]GIFaC`8;OGI5
FbZKV=Q46G\:<5W=QOK5;C25(:<:.=Q4DCDFa8%ObO¹_?8QU8;FHOa8;SOb=YC2Fb49C2JFHGDK2
D
D
D
DE
F F
FG H=I6JKMLON2POQRK(S
T*UWVYXZ [
N]\^N]_`
a
[%b
e0ZFbG6Fa8;OHFb%8%GIFH5(Z¢8%ZNW G6=Q4I:<FHZN8;G6Fb5UZ¢KV= TJ=QZC2=%Kk8%4I=Õ8;Z¢Fb:<MN5U4IGD8%ZG?M8;4IG5;8;Z Fb:<MOb=Q:=QZGD8;G6Fb5UZR
MN8%4IGIF C2JO8;4IOH_\E=`Z 5(4IFbZ7\FbG6EC]5(:<MOH=Q^< hmeC2Fb49C2JFHGDK2AZGIE=5UGIE=Q4hEN8%ZNWR\E=QZ!5(46FHZ7
\FbG6E8~SN=QEN8QFH5(498;OX:<5W=QORGIE=%KV="GIFb:.FbZ7ÕC25(ZNKFaW=`4D8;G6Fb5UZNKp=`FbGIE=Q48;46=Fb7UZ5(46=%W 5U4<8%4I="=Q^M4I=%K6KV=%W
WFdc=`4I=QZGIOH_T} =?:.5W=QOGIE=YEN8;49W\8%4I=FbZFHGIFa8%ObFH%8;G6Fb5(Z"K= mJ=QZNC2=YJNKVFHZ7qGIE=?G6Fb:<FHZ7KVJSÂ=QOH=Q:<=QZG\5;
GIE=kC]5(:<MN5(Z=QZG`
XJ4YC25(:<MN5UZ=QZG:<5W=QO W=QMN=QZNWKE=L8LFbOH_q5(ZGV5qM4I5UM-=`4IGIFH=%K2R5UZ=p465(: T_ZCiE465(Z5UJNKkg8;GD8
OH5;e5;78%ZNWGIE=~5UGIE=Q44I5(: KV_ZNCDE4I5UZ5(JNKqC2FH4DC2JFbGW=%KFb7UZ\e0ZMN8;46GIFC2JOa8%4QRFbG<F K8UKIKJ:<=%W
GIE8;G?8%ObO$5UMN=Q4D8%GIFb5UZNK?8;46=MN=Q46Fb5WF CY58(KFbZ¢gfål>+hifl(ljhk7g8;ZNW~GIEN8%GkG6E=FHZMJG9Kh8;ZNW 5UJGIMJGDKh5;X8
C25U:<MN5(Z=QZGgCQ8;ZSN=CQ8;OC2JOa8%GI=%WqSN8(K=%W~5(Z 8<KVFHZ7(OH=C2Ob5CDR8(K\FHGIEKV_ZNCDE4I5UZ5(JKC]Fb4DC]JFbG9Klfål(nhe0Z
5(G6E=Q4!5U4DWK]RQ!=\8UKIKJ:<=$G6EN8;G=%8(CDEYC25(:.M-5UZ=QZGMN=Q4V5U4I:qK8XC2=Q46GD8;FHZYC2_C]ObFaC5(MN=Q498;G6Fb5(Z?FHZNW=QMN=QZW=QZG
5;ÍGIE=gW8%GD8R8%ZNWpG6EN8;GGIE=\G6Fb:<FHZ7X5;FbZMJG8%ZNW5(JGIMJG=QT=`ZG9K$CQ8;ZSN=C`8;OaC]JOa8%GI=%Wk46=QOa8%GIFbT=GI5hGIEFaK
C2_C2ObFCA5(MN=Q498;G6Fb5(Z~JKVFbZ7<8KVFHZ7(OH=?C2OH5CiNB :<5(46=5U4I:q8%OWFaK6C2JNK6KVFb5UZ5%GIE=LKV=?C]5(ZNKGI4D8%FbZGDK\FaK\7(FHT=QZ
FbZmf¹>2shRnf¹>Qojh
ÃÃ ²oQã]ã+pBq
!E=?G!5U0KJS=QOb=Q:.=QZGXC]5(:<MN5(Z=QZG9K2RNGI5U7(=QG6E=Q4h\FbG6E8 h5;cJNKV=]JOG6Fb:<FHZ7.KVJS465(JG6FbZ=LK2R
5jc=Q4.KV=`T=Q4D8%O!M498(C2G6FaCQ8%OX8(WU8;ZGD8%7(=%K] !E=C]5(:<MN5(Z=QZG9KkZ=Q=%WZ5(GSN=~W=%K6C24IFHSN=%W FbZGI=`4IZN8%ObOb_ 8;G8
7T8%GI=Ob=QT=`O0BAZNWGIE=KV=QMN8%4D8%GIFb5UZ 5;YJZNC2G6Fb5UZNK<:q8;T="FbG<=%8UKV_G65 CDEN8%Z7(=GIE=6GI=%CDEZ5UOb5U7(_ 5;
GIE=kKFb:JOa8%GIFH5(ZObFbS4D8;46_T 5(:<MN5UZ=QZGDK5(4XWF9c=Q4I=`ZGMJ4IMN5 KV=%K]R-=T7C2Fb49C2JFbG6ÂOH=QT=QONW=%KVFH7(Zq5(4!5U4I:q8%O
T=Q46F9CCQ8%GIFH5(ZR8;46==%8UKVFHOb_~W=QT=QOb5UMN=%W 5UZNC2=GIE=?G6Fb:<FHZ7G65T5(OHS-5%^EN8(KSN=Q=QZ=Q^M4I=LKIKV=LWFbZ8qKVJFHGD8%SOb=
GI=LCiEZ5(Ob5U7(_T !E=A:.5W=QON8%OaKV5Y8UW8;MG9K=QObOG65hGIE=XG_MFCQ8;OKVG98;7U=%KFHZG6E=XW=%KFb7(ZM465C2=%KIK]RSN=Q7UFbZZFHZ7
8;G 8 SOb5CDÂOH=QT=QOX8;ZWW=%C25U:<MN5TKVFHZ7 W5%\Z G65¢C2Fb49C2JFHGDK2$}=~W=Q:<5(ZKVGI498;G6=GIEFaKJG6FbOHFbG_\FbG6E8%Z
=Q^8;:<MOb=TR8?CDEN8;Z7U=hS-=`GV=Q=QZqSOH5CiÂOH=QT=QO8;ZW C]Fb4DC]JFbG6ÂOH=QT=QONW=LKVFb7UZ
!E="W5(: 8;FbZ5;g4I=L8;ObGIFH:<=WFH7(FbG98;OcKVFb7UZN8;O\M4I5C2=%K6KVFHZ7~EN8(KkFHZNKVMFb4I=LW ZJ:<=Q4I5UJNK=Bc5(46GDKkGI58%FaW
W=%KFb7UZ=Q4DK]R%C2=Q46GD8;FHZOb_X:<5U4I=GIEN8%Z?CQ8%ZkSN=M4I=%K=QZGI=%WAE=Q4I=@]!=4I=LKVGI46FaC2G5(J49KV=QOHT=%KGI5X8!=Q\EFaCDEhEN8QT=
WFH4I=%C2G6Ob_FHZNJ=`ZNC2=%Wk5UJ4$!5U4I(}=XC2FbG6=\3$GI5UOb=Q:_ fåth0R%\EFaCDEkFH:<MOH=Q:<=]ZG9KÖT_ZNCDE4I5UZ5(JNK8%GD8hOH5;
7(498;MEK\WFb46=%C2GIOH_TRU8;ZNW f¹>(>*h f> *hR8h:JObGIFHÂM4I5C2=%K6KV5U4$=QZFH4I5(Z:<=QZGSN8UKV=%W5(Z<G6E=!#"$&%$'
f>`njhK_ZNCDE465(Z5UJNKÖO8;Z7UJN8;7U=TRU8(KGV5XKV_KVG6=Q:qK5U4W=QT=QOH5(MFHZ7XKVFH7(ZN8%ObM4I5C]=%KIKFbZ7g8;MMObFaC`8;GIFH5(ZNKS8(KV=LW
5(ZqG6E=JNK=5%$M4I5(7U4D8%:<:q8;SOb=gC25(:<MN5UZ=QZGDKKVJNCDE"8(K\m3 M465C2=%KIK5(49K2NFbT=`\FaKV= R 5U4XKV_ZNCDE4I5UZ5(JNK
C2FH4DC2JFHGhW=%KFb7UZGIE=`4I==Q^FKVGhG!5m5Â4I=`Oa8;G6=%W7gKV_KVG6=Q:qK]R 8;G6E=%W498;Obe0 efål*hc8;ZNW G6E=.3 EFaW=Q5ÕKV_KVG6=Q:
f3)(jhR\EFaCDEJNKV= 8 C25U:<MN5(Z=`ZG<:.5W=QOG6EN8;G"FbZNC2OHJNW=%KEN8;49W\8%4I=QOb=QT=`OGIFH:<FbZ7 KB@GIE=LKV=GV5¢JNKV=
TFHOa8;7U=f>`lh5U48;Ob7U5(46FbGIE: W=%K6C24IFHMGIFH5(Z}= =`:<MEN8UKVFb`=G6EN8;G?G6EFaKhFaK?8;Z 8%4ISFHGI4D8%4I_¢K=QOb=LC2GIFH5(ZR8(K
=QT=QZÕC25(ZKVFaW=Q4IFHZ7dJKVGG6E=?W5U:q8;FHZ5%!EFb7(EÂG6E4I5UJ7(EMJG?K_ZNCDE465(Z5UJNKKV_KVG6=Q: W=%KFb7(ZÍRGIE=`4I=?8%4I=
:q8%Z_:<5W=QOK!8%ZNW =QZFb4I5UZ:<=QZGDK]
*JObG6FbOa8%Z7(JN8%7(= KVFH:JO8;G6Fb5(ZK8UK =QObOg8;46= Z5(GIEFbZ7¢Z=Qh+*~8;Z_*W=%KVFH7(Z=`4DK<C25U:SFbZ="GIFb:.FbZ7
8;ZW SN=QEN8QFb5U4D8;OKVFb:JO 8;GIFH5(Z JNKVFHZ7¢ -, GI5U7(=QG6E=Q4<\FHGIE XR!5(4qJNK=KVFH:<FbO8;4C25U:SFHZN8;G6Fb5UZNK5;
M465(M46Fb=QG98;4I_Oa8%Z7(J8;7(=LK2,A5%!=`T=Q4QRG655UJ4?Z5;\OH=%W7U=<GIE=LKV=.C25(:SFbZ8;GIFH5(ZNKh8%4I="8(WE5C(R8%ZNWW5
Z5UGASN=QZ=+CNG!4I5U:Ü8§5U4I:q8%OgÂS8(KV=LW 4D8%:<=Q5(4I
BGI=`48S4IFH=2ÍWFaK6C2JNKIKFb5UZ5%GIE=X8UWU8;ZGD8;7U=%K5%!R 8;ZNWFHGDKOHFb:<FHGD8%GIFb5UZNK\E=QZ.8;GIG6=Q:<MG6FbZ7XGI5
8;MMOb_?FHGG65h he$C2FH4DC2JFbGDK]R(!=XM46=%KV=QZG$5UJ4\C25U:<MN5(Z=`ZG$:.5W=QO0U} =XGIE=`ZM46=%KV=`ZGK=QT=Q498;O8%:<FbOHFb=%K
5;OHFbS498;4IFH=%K!SN8UKV=%W5UZGIEFaKXC25(:<MN5UZ=QZGA:<5W=QO0B GI5T5UObSN5%^5%\KJS465(JG6FbZ=%K\\EFCiEÕ8;4I=YE=QOHMJO5(4
SJFHOaWFHZ7~GIE= G6Fb:<FHZ7~KJS=QOb=`:<=QZG fl(oh\FaKkFbZGI465WJNC2=LWR$GIE=`Z 8%MMOHFb=%WGI5GIE=C]5(ZNKGI4IJC2GIFH5(Z 5%h8
KVFH:<MOH=qKV_KVG6=Q:~}=YCZFaKE S_ M4I=%K=QZG6FbZ78%Z=Q^8;:<MOH=TR$C]5(:<MN5(Z=QZG9K5(4:<5(G6Fb5UZ FaW=Q5~FH:q8;7U=
C25U:<M4I=LKIKVFH5(Z
.
! "$#&- / 10
!E=qT_ZNCiE4I5(Z5(JNKh8%GD8qOb5% 5Vm;7X7(498;ME5c=Q4DKh8;Z=QOH=Q7T8%ZGSOb5CDOb=QT=`OW8;G98;2N5%+4I=QM46=%KV=`Z
GD8%GIFH5(Z~5(4hC2=`4IGD8%FbZ~46=%8;OHÂG6Fb:<=YAFH7(FbG98;O! Fb7(Z8;O3$4I5C]=%KIKFbZ7m503 7X8%MMOHFaCQ8%GIFb5UZNK2FaK8<U8;46Fa8;ZG
5; GIE=YGI4D8UWFbG6Fb5UZN8;OÚW8;G983N5% 7(498;ME f¹>Bhifn*h\E=`4I=kG6E=?8%:<5(JZG\5%\W8;GD8.C25(ZNKJ:<=%Wq8%ZNW M465WJNC2=LW
S_ =L8(CDE Z5W=k5(4g8;OHOFHGDK\FbZMJGDKX8;ZNW5UJGIMJGDK2RNFaK CN^=%W FHZ~8UWU8;ZNC2= 8%GD835; 7(4D8%MENKh8;46=k5%GI=QZ
JNK=%WFbZ¢KFb7(Z8;O\M465C2=%KIKFbZ7~G65~:<5W=QO4I=%8%ObGIFH:<=8;MMObFaC`8;GIFH5(ZNK]RSN=%CQ8%JNKV=qG6E=Q_5jc=Q4.8;Z¢FbZGIJFHGIFHT=TR
FaKVJ8;ObOH_5(46Fb=QZGI=LW8%MM4I5 8(CDE f4*h0
BAZ 8;MMObFaC`8;GIFH5(Z¢=Q^M4I=LKIKV=LW 8UK8%Z g 7(498;ME EN8(K8~M4IFH5(4IF\SN=Q=`Z W=%C25(:.M-5 KV=%WFHZG65~:q8;ZN8%
7(=L8;SOH=<KJSM4I5USOb=Q: K2R=%8UCiEMN=Q4V5U4I:<FHZ7q8"WFaKGIFbZC2G5(MN=Q498;G6Fb5(Z @$8;GhG6E=<K68;:<=GIFH:<=TRG6E=JZFbG_~5;
8;Zq5UM-=`4D8;G6Fb5UZ 5U4!5%Ú8kSOb5CD?5; W8;G98kFaKM4I=%K=Q4IT=LW"!EF KM465;FaW=%K:<5WJOa8%4IFbG_§8;ZNW<GIE=MN5TKIKFbSFHObFHGV_
block DCT
Input
Output DCT
Input
Output
pixel
1 64
1 64
FH7(J46=>>¢Z5W=§8;G\SOH5Ciq8%ZNW MFb^=QOOH=QT=QO
5;W=%K6C24IFHSFbZ7"8%Z¢8;MMObFaC`8;GIFH5(Z 8;GYWFdc=`4I=QZGhOb=QT=QOK5%X8%SNKVG64D8(C]GIFb5UZ$,X=QZNC2=8qW=%KFb7UZ=Q4h!5U4IKFbZ8
:<5U4I=<ZN8%GIJ498;Og8;ZNW¢FbZGIJFHGIFHT=<K=QGIG6FbZ7f\ GIFH:<FbZ7~C25UZNKVFW=Q4D8%GIFH5(ZNK?W5Z5UG=QZGI=`4?FbZGI58;Z*
W=%K6C24IFHMGIFH5(Zq5(MN=Q498;GIFH5(ZNKg8;4I=§W=%K6C24IFHS-=LW MJ46=QOb_.FbZqGI=Q46:qK!5; GIE=QFH4\SN=QEN8QFH5(4`R-Få=TFbZqGI=Q46:qK!5; GIE=
FbZMJGDK #" q8;ZNW¢5(JG6MJG9K j" B (} = C25(ZNKFaW=`4?5(J4SN=QEN8QFH5(498;O\:<5W=`OG65 SN="8;Z*
7(498;MEÍ
BAZ~7(498;MEÕCQ8;Z"SN=k8%ZN8;OH_`=%W<GI5?=%KGD8;SObFaKEq7(5T5WSN=QEN8QFb5(4 f¹>Qrhe0ZqMN8;46GIFaC]JOa8%4QR8?GI498;ZNK0=Q4
:q8%GI4IFH^qCQ8%ZSN=k5(46:<=%W4I5U: G6E=kFHZMJG9KA8%ZNW5(JGIMJG9KA5;c8%ObOZ5W=%K]R\FbG6E\EFCiEqFbGgCQ8%Z~S-=Y=%KVG98;
SOHFaKVE=%W<GIEN8%GAG6E=kFHZMJGX8%ZNW5(JG6MJGXSJc=Q49K\FHObOSN=kSN5(JZNW=%WXZ=?C`8;Z~8%OaK5<8%ZN8;OH_Q=hG6E=k7U4D8;ME
5(4XOb5T5UMNK\\FbGIE5(JGX8%ZFbZGI=`4IT=QZFHZ7YW=QO8L_ R\EFCiEq!5UJOaW<FH:<MOb_8W=%8UWOb5CD.WJ4IFHZ7=Q^=LC2JGIFH5(Z
e0Z<GIE=X4I=`:q8;FHZNW=Q4$5%$G6EFaKK=%C2GIFH5(ZRT=M4I=LKV=QZGGIE=km :<5W=`OFbZ<7U4I=%8%GI=Q4cW=QG98;FbOR;5(OHOb5%!=LWpS_
8;Z8%ZN8;OH_KFaK5%FbGDKObFb:.FbGD8%GIFH5(ZNK]RQ8;ZW?8;Z?FbZGI465WJNC2G6Fb5UZ?GI55UJ48;MM4I5 8(CDEp5U4$8%MMOb_FbZ7k~C25UZNC2=QMGDK
GI5GIE=kW=%KVFH7(Zq5; KV_ZNCDE4I5UZ5(JNK\EN8%4DWc8;4I=
e0Z G6E=q:<5W=QOR8"KVFb7UZN8;OM465C2=%K6KVFbZ7~8;MMObF CQ8;G6Fb5(ZFaKgW=%KIC]4IFbSN=%W~FbZGI=`4I:qK\5;l#+
R0nGI498;ZNK0=Q4DK
8;ZWp5UM-=`4D8;G6Fb5UZNK2 !E=\ZJ:S-=`45% #" =`Ob=Q:<=`ZG9K-Z=Q=LW=%W5(48%Z5UM-=`4D8;G6Fb5UZG65kC]5(:<:<=`ZNC2=URQ8;ZW
GIE=kZJ:SN=Q4\5% "B=QOb=`:<=QZGIK4I=%KJObG6FbZ7?4I5U: 8%Z~5(MN=Q4D8%GIFH5(ZR8%4I= CN^=%W"8;GhW=LKVFb7UZ~GIFH:<=TJ46
GIE=Q4I:<5U4I=TRTG6E=ZN8%GIJ46=5%$G6E=%K=M4I5WJNC]=k8%ZNWqC25(ZKVJ:<=X=QOH=Q:<=QZGDKF K!Z5(G C^=%W$GIE=`Fb4!7U4D8%ZJO8;46FbG_
CQ8%ZU8;4I_~4I5U: KVFHZ7(OH=<!5U4DWKh5(4kMFb^=QOaK]RGI5"SOb5CDKh5;g8%4ISFHGI4D8%4I_ KVFHQ=TR46=QM4I=LKV=QZGIFHZ7<5(4k=`^8%:<MOb=
=QZGIFH4I=hFb:q8%7(=%Klfl (h0 !E=?C25UZNKVJ:<=h=QOb=Q:.=QZG9K8;4I=?SJc=Q4I=%W"8;GXGIE=YFbZMJGAG65q8;Z~5UMN=Q4D8%GI5(4gJZG6FbO8%Z
FbZMJG\GIE4I=%KE5(O W FaK!46=%8(CDE=%W@GIE=k5(MN=Q498;G65(4XFaK\GIE=QZ (R5U4KGD8;46GI=%We0ZqGIE=Y8%SNKVG64D8(C]GA:<5W=QO0RGIE=
4I=LKVJOHGDK8;46=AG6E=QZ.8LU8%FbOa8%SOb=\FH:<:<=%WFa8;G6=QO¹_TRQF0=T%GIE=XM4I5WJNC2=X=QOb=Q:.=QZG9K8%4I=XM4I5WJNC2=%W\FHGIEZ5YW=QO8L_
!E=hZJ:SN=Q45; C25UZNKVJ:.=A=QOH=Q:<=QZGDKZ=Q=%W=LWGI5?O 8;JZNCDE"8;Zq5(MN=Q498;G6Fb5(ZÍRNW=QMN=QZNWK!5UZqGIE=h5(MN=Q498;
GIFH5(Z"8;ZW 5(Z"GIE=g7(4D8%ZJOa8;46FbG_<5%$G6E=h=QOb=Q:.=QZG9K2T5U4A=Q^8;:.MOb=TR 8pG!5U0WFb:<=QZKVFb5UZN8;OWFKIC246=QGI=C25TKFbZ=
GI498;ZNK05(46: 50 7\EFaCDEk4I=mJFH4I=%K8ASOH5CiY5;Ín;^nAMFH^=`OaK8(KFHZMJG`R(:q8Q_SN=\4I=QM4I=%K=QZG6=%WFHZ?C25 8;49KV=Q
7(498;FHZW8;GD8 5; 8(K\C]5(ZNKJ:<FbZ7>SOb5CDG65KVGD8%4IGM4I5C2=LKIKVFHZ7X4`R8;GX8h:<5(46=ACZ=h7(4D8%FbZRGIE=
:q8Q_S-=Y4I=QM4I=%K=QZG6=%W<8UKAC25UZNKVJ:<FbZ7t%sMFb^=QOaKS-=]5(4I=§KVG98;4IG6FbZ7!E= C4DKVGX4I=`M4I=%K=QZGD8;G6Fb5UZ8UKIKJ4I=%K
GIE8;GX8;OHOG6E=hFbZMJGDK\FHObOÍ8;4I46FbT=g8;G\G6E=YKI8;:.=AFHZNKVG98;ZGQR\EFbOb=gGIE=YKV=LC25(ZNW4I=QM46=%KV=`ZG98;GIFH5(Z<FH:<MOHFb=%K$8
SJc=Q46FbZ7Y5;FHZMJG=QOH=Q:<=QZGDKJZGIFbO8%ObONEN8QT=\SN=Q=QZ<46=%C2=QFHT=%WUeZ.FH7(J46=k>g8;Zg Z5W=A5U4\8Y
FaK!7UFbT=QZ 8;Gg8pSOH5Ci.8;ZW8;Gg8kMFH^=QOOb=QT=`O0
3 1
1 2
2
3 c
d e f
a b
Fb7UJ4I=Yl>NB 7U=QZ=Q46FaCAG6E4I=Q=hZ5W=?W8%GD8 5; 7(4D8%ME
{y% w<¡zx%zÚ mNy%z w
BAZm 7(498;MEqFK!8kC]5(ObOH=%C2G6Fb5(Z5;ÚC]5(ZZ=LC2GI=%WZ5W=%K]8(CDE<Z5W=h46=QM4I=LKV=QZGDK8?KVMN=%C]F9CC\5(MN=Q498;GIFH5(ZR
GIE=\C25U:<MOb=`^FHGV_5;N\EFaCDEkW=QMN=QZNWK5UZkG6E=!OH=QT=QO%5;W=%KIC246FbMG6Fb5UZk5;GIE=8(K6KV5C2F8;G6=%WJZNC2G6Fb5UZN8;OSOb5CD
!E=Y5(MN=Q4D8%GI5U4\FbOHO5(MN=Q498;G6=k5(ZKFb7UZN8;OK\EFCiE"C25UZG98;FHZ8%Z~FbZCZFbG6=hKVG64I=%8%: 5%U8;OHJ=%K2XMN=Q498;GIFH5(ZNK
:JNKVG8%OaK5kSN=AFHZNW=QMN=QZW=QZGQR(Få=TT8%ObOFHZG6=Q4D8UC2GIFH5(ZNK$SN=QG!=`=QZ?5(MN=Q498;GI5U4DK!:JNKVGÚS-=gKVMN=%C]F9CN=%W?S_?:<=%8;ZK
5;ÍGIE=XKGD8%GIFaC!G64D8%ZNK=Q49K2 !EFK _Fb=`OaWK87(4D8%MEFbZ?\EFCiE8%ObO5UM-=`4D8;G6Fb5UZNK!8%4I=\Z5W=LK2R8;ZNW8;OHOGI498;ZNK0=Q4DK
8;46=8;4DC`KÖSN=QG!=`=QZZ5W=LK2 !E=KVFb7UZN8;OH5; 7(4D8%MENKM4I=%K=QZG6=%WAS_h=Q=8;ZW1*=%K6KV=Q49KICDE:<FbG6G8;4I=CQ8%ObOH=%W
# !"#GI5=Q^M4I=%K6K!GIE=8(C]G\GIEN8%G8%Z5(MN=Q498;G65(4XFaK!FbZT5(T=LW\E=QZ"8?M4I=QKVMN=%C]F9CN=%W<ZJ:S-=`4!5;
Z=Q U8;ObJ=%Kh8;4I=8QU8;FHOa8%SOb=.8;GY8;OHO$FbZMJGDK]}==Q:.MEN8(KFbQ=YGIEN8%GhGIE=GIE46=%KVE5(OaW5(4h=%8UCiE~FHZMJG`R8(K
!=`ObO\8UKpG6E=qZJ:SN=Q4h5;gFbZMJGDKC25UZNKVJ:.=%W8;ZWG6E=qZJ:SN=Q4Y5;g5(JG6MJGDK?M465WJNC2=%WR$FaK CN^=%WFbZ
8(W(8%ZNC2=§8(KXKVE5%\ZqFbZ"FH7(J46=>U
ww2x%{(
}E=QZW=QT=QOb5UMFbZ78<KV_ZNCDE4I5UZ5(JNKgW8;G98 5; 8%MMObFCQ8;G6Fb5UZR-FHGAFKFH:<MN5(46GD8;ZGXGIEN8%GGIE= 7U4D8;ME
EN8UK8XS-5UJZNW=LWC2_C2OHFaCKICDE=%WJOb=T !EF KFbZ?G6J4IZ?FH:<MOHFb=%KNGIEN8%G=L8(CDEkZ5W=gCQ8%Z?S-=\FHZT5UT=%Wk8XS-5UJZNW=LW
FbZGI=`7(=Q4$ZJ:SN=Q4$5;G6Fb:<=LK2RU8LGI=`4!\EFCiE?FHZMJGc8;ZNW5UJGIMJG!SJ c=`4DK\FHObO46=QGIJ4IZ<G65k8hM4I=`FH5(JNKKVGD8%GI=
5; JObOHZ=%K6K 5(4=Q^8;:<MOH=TR%F=AE8LT=XG!5hZ5W=LK!\FbGIE.8kC]5(:<:JZFCQ8;G6Fb5(Z§W=QMN=QZNW=QZNC2_?SN=QG!=`=QZ
GIE=Q:~R!=C`8;Z~MN5TK=<GIE= TJ=%KGIFH5(Z~\E=QG6E=Q4FHGAF KAMN5TK6KVFbSOb=GI5"CQ8;OHO=L8(CDE~Z5W=.8 CNZFHGI=?ZJ:SN=Q4X5;
GIFH:<=%K]R28%ObOH5;\FHZ7g8AC25U:<MOH=QGI==Q^CiEN8%Z7(=5%NGIE=cKVMN=%C2FdCN=%WZJ:SN=Q45;W8;GD8R;\FHGIE5UJGÚ8(CQC2J:JO8;G6Fb5(ZX5(4
KVG98;46(8%GIFH5(Z<5UZ<GIE=\M8;4IG5;Í=QFbG6E=Q4$Z5W=T !E=XM465(MN=Q4IG_?5%=Q^FaKGI=QZNC]=!5;Ú8SN5(JZNW=%W<C]_C2OHFaCKICDE=%WJOH=
FaKXCQ8%ObOb=LW #09#+,+ *kFbZmf>`rh0N=Q= *=%KIK=Q4DK6CiE:.FbGIGM4I5%FaW=YC25UZNWFHGIFb5UZNK5U4C25UZNKVFKVG6=QZNC2_TRS8(KV=LW
5(ZÕ8kGI498;ZNK0=Q4A: 8;GI46Fb^?\EFCiEq46=QM4I=LKV=QZGDKGIE=?¢7(498;ME
hz !¡axD {T ¡ ¥x w -y.{T ww2x%{(
5(4X8k7UFbT=QZq7(498;MEÍR!=5(JOW OHFbT=XGI5 CNZW 8kMN=Q46Fb5WFCKICDE=%WJOb= yTeÂÚKVJNCDE"8?KICDE=%WJOb=X=Q^FHGDK]R
!=YCQ8%Z"KV5(OHT=Y8K_KGI=Q: KVJNCDE"8(K\GIE=h5UZ=k7UFbT=QZ<FHZ"Fb7UJ4I=Yl !E=kZJ:SN=Q45%=QOb=`:<=QZGDKM465WJNC2=LW
8;ZWC25UZNKVJ:.=%Wp5(4X=%8UCiE<OHFbZFaK\4I=`M4I=%K=QZGI=%WS_GIE=h=Q^M4I=LKIKVFH5(ZNK+>
!"
#
"$&%
(') * +$,'-
.
/'0)1* 2/'43
5
,'- * 6/'73
8"9"
:
% + (
( 5 6
. ( 2
FH7(J46= 3> 5(MN5(OH5(7(_ *~8;G64IFb^.8(K6KV5C2F 8;G6=%W\FbG6EFb7(J4I=hl
\E=Q46=
'
4I=`M4I=%K=QZGDKGIE=ZJ:SN=Q45%NGIFH:<=%KG6EN8;GZ5W=NFaK %} =cCQ8;ZYGIE=QZYT=Q4IF¹_GIE==mJN8%ObFHGV_
SN=QG!=Q=`Z<=QOb=`:<=QZGDK$M4I5WJNC2=%Wq8;ZW =QOH=Q:<=QZGDKC25UZNKVJ:.=%W'>
!"
#"$ % ,')
+$,'- * (
.
,')
2!,'43 * (
5
/'-
6,'43 * ( 8"9"
:
} =XC`8;Z.8(KIK5C2Fa8%GI=g8 RB d1
R+08UKKE5%\ZFHZ<Fb7(J4I=<3A\FHGIEGIE=\7U4D8;ME<7(FHT=QZkFHZFb7UJ4I=
lB+C25UObJ:<Z.FaK8UKIKV5C]Fa8;G6=%W\FbG6E~=%8(CDEZ5W=TR8;ZNW~8465% \FHGIE"=%8(CDE=%W7(=T !E=?=%W7U=%K\EN8QT=kSN=Q=QZ
Oa8%SN=QOb=%WkFHZ<8%Z<8%4ISFHGI498;4I_k8UKVEFH5(ZR8UKKE5%\Z<FbZGIE=\ObFbG6GIOH=!SN5%^=%K$FHZG6E=XFb7UJ4I=gl !E= 5!7\=QZGI4I_
W=BCZ=%K\GIE=YZJ:SN=Q4!5%W8%GD8=Q^CDEN8;Z7U=%W<SN=QG!=Q=QZqZ5W=8%ZNWNNeÂ8pZ5W=qC25(ZKVJ:<=LK\W8;G98p5UZ
=%W7U=-G6E=\U8;ObJ=\FaKZ=`7T8;G6FbT=@Q5UGIE=`4I\FaK=\FbG$FKÖMN5 KVFbG6FbT=TR%5(4= TJN8%OG65Q=Q465FN=LW7(=hFaKZ5(GC25UZZ=%C]GI=%W
GI5Z5W=I
=Q=8;ZNW-*=%K6KV=Q49KICDE:<FHGIGNKE5%GIEN8%G8!Z=%C2=LKIKI8%4I_hC]5(ZNWFHGIFH5(Z5(4G6E=$=Q^FaKGI=QZNC]=$5;8!U8;ObFWhKV5(OHJGIFH5(Z
KICDE=%WJOb=TR]FaKGIEN8%G
'
% 5(7
*
>UR;\E=Q4I=:q8;G64IFb^ FKÖG6E=:q8;G64IFb^X5;5UJGIMJGDK8;ZNWkFHZMJG9KÖSN=QG!=`=QZ
GIE=kWF9c=Q4I=`ZG\Z5W=%K5%5(Z=k7(498;MEÍR8%ZNW
FbGDK\ZJ:SN=Q45%Z5W=%K/fål>+h fålUljh0Ne0Z<8(C]GQRF 8KV5(OHJGIFH5(Z y
=Q^FbG9K2RFHG\\FbOHOSN=Y8pZJObOT=%C2G65(45U4AG6E=hGI498;ZNK0=Q4\:q8;G64IFH^>
y
* ("!
FbT=`\FaKV=c8;Z_k:JObG6FbMOH=$5;ÍGIEFKZJObOT=%C2G65(4\FbObO8;OaK5SN=8gKV5(OHJGIFH5(ZRT_Fb=QOWFbZ7X8g8%:<FbOH_5;ÖKV5UObJG6Fb5(ZK2
!E=%K=XKV5UObJG6Fb5(ZK$C25(464I=%KMN5(ZNW?GI5h8gKVFbZ7(Ob=5(4:JObG6FbMOH=FHGI=Q498;GIFH5(ZNK5;GIE=cKV_KVG6=Q:MN=Q46Fb5WTe0ZGIJFHGIFHT=QOb_UR
5(Z=XCQ8;ZK=Q=\GIEN8%GGIE=Q46=!:JNKVG=Q^FaKG$8KFbZ7UOb=!8%:<FbOH_5;ÍKV5UObJG6Fb5UZT=%C]GI5(49K2R%SN=%CQ8;JKV=\GIE=XKV_KVGI=`: :JNKG
SN=8;SOH=?GI5<46JZ5(4g5(Z=?5U4:.5(4I=hMN=Q46Fb5WK]R\EFbOH=?8%GG6E=?K68;:<=YGIFH:<=TRG6E=8;SKV=QZNC]=?5;cC25(ZWFbG6Fb5(Z8;O
C25U:<:JZFaC]8;G6Fb5(ZK FH:<MOHFb=%K$GIE8;GXGIE=Q46=hFaK!5(ZOb_<5UZ=kMN5TK6KVFHSOb=Y=Q^=LC2JGIFH5(ZqK6CiE=Q:<=T !E=YKV_KVG6=Q: FHGDKV=`O
:q8Q_hSN=h8hKVJSNK_KGI=Q:+5%8hOa8;467(=Q4Ú7(4D8%MERFbZ\EFaCDECQ8(K=AG6E=X:<FbZFH:?J:*M-=`4IFb5W5;G6E=XOa8;467(=Q47U4D8;ME
\FbOHOSN=Y8k:JObGIFHMOb=\5%$G6E=hMN=Q4IFH5WK5%8%ObOÍKVJS7U4D8%MENK2 !EFaK\CQ8%ZqS-=YK=Q=QZqFbZGIJFHGIFHT=QOb_4I5U: GIE=8UC2G
GIE8;GhF#
8%ZNW$&%§8;46=G5KJS:q8;G64IFC2Fb=%K\4I=`M4I=%K=QZGIFbZ7qKVJSKV_KVGI=`:qKA5; $RF¹!G6E=Q_KEN8;46=<8<ObFHZR
GIE=Q_<\FbOHOKEN8;46=?8kMN=Q4IFH5W \EF CiE.:JNKG\K68;GIFK_qSN5(G6EZJObOT=%C2GI5U4DK]
e0Z<5(49W=Q4\GI5?46=QZNW=`4G6E=YCQ8;OC2JO 8;GIFH5(ZNK:<5(46=A: 8;ZN8%7(=%8%SOb=TRT=\FbOHO-7U=QZ=Q498;OHOb_.C25(ZNKFaW=`4!5(ZOb_GIE=
Ob=L8(KVG\5%GIE=kK5(OHJGIFH5(ZqT=%C2G65(4DK!5%$G6E=YKV_KVG6=Q: 5Â5U4KJSNK_KGI=Q: 7ÚJZNW=`4XC25(ZNKFaW=`4D8;G6Fb5UZ
'( )(*,+-*.( 0/21 3
!E=m 4I=QM46=%KV=`ZG98;GIFH5(ZE8(KkObFH:<FbG98;G6Fb5(ZK2RG6E=<:<5 KVGJZNW8;:.=QZG98;OSN=QFbZ7~GIEN8%G?FbG?C`8;Z5UZOb_SN=
8;MMObFH=%WpG65?8hObFb:.FbGI=LWkKVJS0C]Oa8(K6K5%ÚKVFb7UZN8;ONM465C2=%K6KVFbZ78;MMOHFaCQ8%GIFH5(ZNK]RmZ8;:<=QOH_kG6E5TK=A\E=`4I=G6E=W8;GD8
GI498;ZNK0=Q4DKqCQ8%Z SN= KVG98;GIFCQ8;OHOb_ KVMN=%C2FdCN=%We0Z 8UWWFbG6Fb5UZR!S46=%8;FbZ7¢G6E=C25(:.MOb=QG6=~8%MMObFCQ8;G6Fb5UZFbZGI5
KVJSÂM4I5(SOb=Q:qK]RN8(KA46=QM46=%KV=QZGI=LW S_qGIE=YZ5W=%KX5;c8;Zg 7(498;MEÍR:q8Q_<ObFH:<FbGG6E=kMN5TK6KVFHSFbOHFbGIFH=%K!5(4
7(OH5(SN8%OA5UMGIFH:<FbL8;GIFH5(ZÚBAMM465T8UCiE=LKKJNCiE 8(KG6EN8;G5; ! f3 (jhR$E5%!=QT=`4QR$8%ObOH5; 8;JG65(:q8%GI=%W
5(MGIFb:.Fb%8%GIFb5UZq5;cKV_KVG6=Q:qK!\EF CiE CNGGIE=T_ZNCDE4I5UZ5(JNKh8%GD8<Ob5% :<5W=`O0RMN8%4IGIFC2JO 8;4IOH_qFbZG6=Q4I: K
5; :<=Q:<5U4I_?8%ObOH5CQ8;G6Fb5(Zmf3>*h0
XFbT=QZ 8~KVJFHGD8%SOb=.8;MMObFaC`8;GIFH5(ZRG6E=Q4I=.FaKk8%Z5(G6E=Q4YObFb:.FbGD8%GIFH5(Z~\EF CiEGI5~JNKY8;MMN=%8%4DKk46=QOb=QU8%ZG>
8(KM4I=%K=QZG6=%WS_=Q= *=%KIK=Q4DK6CiE:.FbGIG`R8;ZNW FH:<MOb=`:=]ZG6=%W~FbZ¢GIE= W5(:q8%FbZ¢5;GIE=
W=%KFb7UZKV_KVGI=`:$' fåth0R8;MMN=%8%4DKSN=QG6GI=Q48(W8%MGI=%W~GI5q:<5W=QObFHZ7<K5;G\8%4I=GIEN8%Z E8;4DW\8;46=T
!EFK!FaK\WJ=hG65?GIE=hSOH5Ci<Z8;GIJ4I=h5;ÚGIE=hG64D8;ZK=Q49KA8%ZNW<5(MN=Q4D8%GIFH5(ZNK]R-\EFCiE"C25U4I46=%KVMN5(ZWC2OH5TKV=`Ob_?GI5
8;ZqFHZMJG\5U4A5UJGIMJG\SJc=Q4X8;ZW8?KVJS4I5UJGIFHZ=?CQ8%ObORm46=%KVMN=%C]GIFbT=`Ob_T(}EFbOb=gSJc=Q4DKX8;ZW KJS465(JG6FbZ=%K
8;46=h!=QOHObKVJFHGI=%Wk5(4\FH:<MOb=`:=QZTG98;G6Fb5(Z?JKVFbZ7?5(Z=h5(4\:.5(4I=gM4I5U7(4D8%:<:q8%SOb=g3 ¾K]RG6E=Q_.8;4I=hMN5T5(46Ob_
KVJFbGI=LW G658W=%WFaC`8;GI=LW eEN8%4DWc8;46=FH:<MOH=Q:<=]ZG98;GIFH5(Z
e0GFKC2Ob=%8%4$GIE8;G!G6E=Q46=CQ8%ZSN=g87U4I=%8%G\W=%8%ON5;KFb:<FHOa8%4IFbG_SN=QG=Q=QZ8;Z" 7U4D8;MEq8;ZNW.8;Z.f\
:<5W=`O-5%Ú8EN8%4DWc8;46=QÂS8(KV=LW KFb7UZN8;OM4I5C2=LKIKVFHZ7KV_KVG6=Q:~Te0Z.8;Z"8;MMObF CQ8;G6Fb5(Z.KVJCiEq8UK:<5UGIFH5(ZFW=Q5
C25U:<M4I=LKIKVFH5(ZFbZ<46=%8;OGIFH:<=TRUC25(:<MOb=Q^Y5(MN=Q4D8%GIFH5(ZNK\KJNCiE 8(K\8?WFKIC246=QGI=gC25TKFbZ=XGI498;ZNK05(46: 50 78%4I=
5;G6=QZMN=Q45(46:<=%W<S_ 8KFbZ7UOb=?W=%WFaC`8;GI=LW C]Fb4DC]JFbG`R\EFCiEqGD8%T=%KX8pSOH5Ciq5%W8;G98<8;GXGIE=FHZMJGg8;ZW
M465WJNC2=%KY8<SOb5CD~5;gW8%GD8"8;GhGIE=5(JGIMJG`!E=<M46FbZNC2FHMN8;O WF9c=Q46=QZNC2=k5U4G6E=.W=%KVFH7(Z=`4FKFbZGIE=
GIFH:<FbZ75%gW8;G98 GI498;ZNK0=Q4DK]3 465WJNC2= 8;ZNW 5UZNKVJ:<=?GIE46=%KVE5(OaWKFbZ¢:JNKVGSN=4I=QMOa8(C]=%W S_~8
KVG64I=%8%:+5;ÍW8%GD8R!5U4DW?S_Y!5(49WR(G6546= N=%C]G$GIE=\5UMN=Q4D8%GIFb5UZ<5;ÍGIE=\E8;4DW\8;46=8%G8f\=Q7UFaKVG6=Q44D8%ZNK=Q4
Ob=`T=QO0eGXFaK\SN8UKVFaC`8;ObOH_"8SN8;ZW\FaWG6E8;ZNW~KGI5U4D8;7U=?M4I5USOb=`: GIE=`4I=?8%4I=QZ åGX=QZ5(J7(E~MFHZNKA5(Z8.CiEFHM
GI5MN8UKIK\SOb5CDK!5%W8;GD88;Gg8?GIFb:.=TR(Z5U4W5T=LK5UZ=h\8;ZGXGI5KVG65(46=?W8%GD8?JZZ=%C]=%KIK68;4IFHOb_T
+ -1 3 + +
XZ="8;MM4I5T8UCiE GI5:<5W=QOHFbZ7Õ8 E8;4DW\8;46=~K_KGI=Q: 8%GG6E="f=`7(FaKGI=Q4 4D8%ZNK=`4OH=QT=QO0RFKkGI5S4I=%8%
W5%\Z<SOH5Ci5(4IFH=QZGI=%Wk5UM-=`4D8;G6Fb5UZNK!FbZGI5YKVFH:<MOH=Q4KVJSÂ5UMN=Q4D8%GIFb5UZNK2RJZG6FbO=%8UCiE5(MN=Q498;G6Fb5(Zq5(4IK$5(Zq8
KVFHZ7(OH=!5U4DW<5; W8%GD8}=hWFKICQ8%4DW<GIEFaK!8%MM465T8(CDERN8UKFHG!_Fb=QO WK8;ZqJZ\Fb=QOW_<8%ZNWqC25(JZG6=Q4IFHZG6JFbG6FbT=
7(498;MEÍR8%ZNW F K\8;OaK58pMN5T5U4:<5W=QON5(4\ hme!C2FH4DC2JFHGDK]
} =§CiE5T5TKV=YFbZNKGI=%8UWGI5:<5W=QOSOb5CDK!5%\W8;GD8.8;GXGIE=§f Ob=`T=QO8UKSN=QFHZ7<GI498;ZNK0=Q4I46=%WK=Q4IF8;OHOb_TR
!5U4DWS_k5(49W A5W=%KFbZ5(J47(498;MEÍR8;ZW<C25(:.M-5UZ=QZGDKFHZ5UJ4!OHFbS498;46_TRT8;46=C]5(:<MN5TK=%W?5;G5kKJS
=QOH=Q:<=QZGDK]R8?GIFH:<FbZ7?C25U:<MN5(Z=QZGX8;ZW~8;Z5UMN=Q4D8%GI5(4`}=kJNK=kGIE=G6Fb:<FHZ7?C]5(:<MN5(Z=QZG\G65<4I=`M4I=%K=QZG
GIE=kGIFH:<FbZ7k5;c8C2_C2ObF CAGI498;ZNK0=Q4QRN\E=QG6E=Q4XFbGXS-=§8;Gh8SOb5CD<Ob=`T=QO5ZN8;G6FbT=?;7c5(4gKV=Q46Fa8;OÚKVG64I=%8%:
50C]Fb4DC]JFbG6ÂOH=QT=QO 79
e0Z5U4DW=Q4G65: 8;T=!G6E=gCiEN8%Z7(=`Â5%Â:<5W=QO=%8UKVFb=`4QR(5UJ4!OHFbS498;4I_Y5;Í=QOb=Q:.=QZG9KC25(ZGD8%FbZNK$SN5(G6E<SOH5Ci
Ob=`T=QON8;ZW C]Fb4DC]JFbG6ÂOH=QT=QOGIFb:.FbZ746=QM46=%KV=QZGD8%GIFH5(ZNK$5(4XWFdc=`4I=QZG5(MN=Q4D8%GIFH5(ZNK]} =Z5(GI=gGIEN8%G\GV_MF CQ8;OHOb_
GIE=!GIFH:<FbZ7\KVJSÂ=`Ob=Q:<=`ZGÍCiEN8%Z7(=LK2R%\EFbOH=!FbZGI=`4IZN8%ObOb_XGIE=!5(MN=Q498;G6Fb5(Z?46=Q:q8%FbZNK8%Z?5(MN=Q4D8%GI5U4$5(Z?SOH5CiK
5;cW8%GD8RGIE=§KI8%:<=Y8(KA5(JO W SN=?JNKV=LWFbZ $'! !Ne0Z"GIE=h5(ObOH5%\FbZ7.KV=%C]GIFb5UZRN!=?W=%KIC246FbSN=h5(J4
f\C]5(:<MN5(Z=QZG:<5W=QO
interface
operator timing sub-element
FH7(J46=s!>B !E46=Q=QMN8;46GFHS4D8%4I_ 5(:<MN5UZ=QZG
' #
XJ4X8;MM4I5 8(CDE~KVMN=%C]F9CN=%Kf\C25U:<MN5(Z=`ZG9KJNKFbZ7.8?KV_ZNCDE4I5UZ5(JNK\GIFH:<FbZ7kKJS=QOb=`:<=QZGQ(}=YC25(:<
MOH=QGI=QOH_YKV=QMN8%4D8%GI=XGIFb:.FbZ7X8UKVMN=%C2G9K 5%8hC25U:<MN5(Z=QZG4I5(:+5UMN=Q4D8%GIFb5UZN8;O8UKVMN=%C2G9K2RT4I= =%C2GIFHZ7XGIE=\JNKJN8;O
C25UZNC2=QMG6JN8;OÚWFKVGIFHZNC2G6Fb5(ZqSN=QG!=`=QZqGIE=<"!+R0n5%8<C2FH4DC2JFHG\8%ZNWGIE= R0n 0n 15;c8C2Fb49C2JFHGQ !E=kGIFH
:<FHZ7qKVJSÂ=`Ob=Q:<=`ZG\F KJKV=%W~GI5qGI498;ZNKFbG6Fb5(ZSN=QG!=Q=`Z8;Z g 7U4D8;ME¢8;ZNW8;Zf\ C2FH4DC2JFbG:<5W=QO0
!E=X5(MN=Q498;GIFH5(Z"KVJSÂ=`Ob=Q:<=`ZG\EFaCDEM-=`4V5(46:qKG6E=JZNC2GIFH5(Z<FK$GI4I=L8;GI=LW8UK!8 6SOa8UCi?SN5%^R\FHGIE5UJG
4I=`7T8;49W5U4$FbG9KFb:<MOH=Q:<=]ZG98;G6Fb5(ZÍ !EFaK8;MM465T8UCiEWFdc=Q4DK4I5U: =Q^FaKVG6FbZ7gKV_KVG6=Q:qK5(4W=`T=QOb5UMFbZ7MN=Q4I
Fb5WFaCC2FH4DC2JFbGDK]RKVJNCDEq8(KB , fXB fål*h0R &! f3 (h0R5(41% fl;shR\EFCiE.JNKV=Z5%\Ob=LW7(=
5;XG6E=FbZGI=Q46ZN8;O$5UMN=Q4D8%GIFb5UZNKkGI5"MN=Q4V5U4I: 8;OHOb5CQ8%GIFH5(Z¢8%ZNW 5(MGIFb:.Fb%8%GIFb5UZN} ==Q:<ME8(KVFHQ=?GIE8;Gh5(J4
8;MM4I5 8(CDEFaK!G98;467(=QG6=%Wq8;GgKV_KVGI=`:<ÂOH=QT=QONf \W=%KFb7(ZÍRN8;ZNW<Z5UG8%GAFHZNWFbFaWJN8;OÍC25(:<MN5UZ=QZG\W=%KFb7UZ
+ * + * *
}=?JNKV=§8GIE46=Q=QMN8;46G:q8 mJ=`GIGI=Y8UKG6E=?KGD8%4IGIFHZ7qMN5(FbZG\5(4h=%8(CDE~C]5(:<MN5(Z=QZG` !E=?:q8 mJ=`GIGI=hFHZ
C2OHJNW=%KGIE=GIFH:<FbZ7XKMN=%C2F9C-CQ8;G6Fb5(ZÍRQGIE=\5UM-=`4D8;G6Fb5UZR(8%ZNWkFbZGI=`4V8(C]= 67(OHJ= ASN=QG!=`=QZkG6E=!FHZMJGQ5(JGIMJG
8;ZW GIE=.5(MN=Q4D8%GIFH5(Z 5Fb7UJ4I=s79A5UGI=GIEN8%GkZ5UG?8;OHOMN8;46GDKk5;XG6E=:q8TJ=QG6GI=?Z=Q=LW SN= CNOHOb=%W~\5(4
=Q^8;:<MOb=TRTGIE=Q4I=FK498;46=QOb_.8;Z_<FbZMJGXFbZGI=Q48(C2=46= TJFb46=%WFÚSN5(G6EFbZMJGX8;ZW 5(MN=Q498;G6Fb5(Z"5CQC2J4g8;GX8
SOH5Ci<OH=QT=QO
!=QOb5% !=gW=%KIC]4IFbSN=XS4IFH= N_?=%8UCiE5;G6E=XGIE46=Q=AM8;4IG9KFHZ<FH7(J46=s !E=gMN8;46G!Oa8%SN=QOb=%W y%zx% Ny
FaK.8;Z 8;4IFHGIE=`:<=QGIFC5(4.Ob5(7UFaCQ8%O5(MN=Q498;G65(4q\EFaCDE*W=%K6C24IFHSN=%KpG6E=~SN=QEN8QFb5(4.5;?G6E=~C]5(:<MN5(Z=QZG`!e0Z
$' *GIEFaKk!5UJOaWSN="CQ8;OHOb=%W8;Z
B i _MFaCQ8%ObOH_TRGIEF KFaK?8ÜKJS465(JG6FbZ=T!E= 5UMN=Q4D8%GI5(4
GD8%T=%KkFbZMJGW8%GD8 FHZ 8%Z8%4ISFHGI4D8%4I_ 5U4I:q8%G 50K68L_ R8 SOH5Ci 5;n ^¢n~!5U4DWK7DR8;ZNW¢_FH=QOaWK4I=LKVJOHGDK
\FbG6E5(JG!8%Z_W=QOa8Q_TRUC25(464I=%KMN5(ZNWFHZ7kG65Y8KJS465(JG6FbZ=gCQ8;OHO0"!E=lR0n 0n1 0
1
5;G6E=gC25(:<MN5UZ=QZG
FaK$M46=%KV=`ZG6=%WpG65hGIE==`^G6=Q4IFH5(4$S_?GIE=Xx <wvÖ9! -x !E=XGIFH:<FbZ7FbZNC]ObJNW=LK$8kCDE=%CDh5(Zq8%ObO
FbZMJGDKG6EN8;GhGIE=Q_~FbZNW=Q=%W~8;464IFHT=?\E=QZGIE=GIFH:<FbZ7.WF 8;7(498;: FHZNWFaC`8;GI=LKAGIEN8%GkG6E=Q_~8%4I==Q^M-=LC2GI=%WR
8;ZW =Q^MObFC2FbGX7(=QZ=Q4D8%GIFb5UZ¢8;ZWKVJMM4I=%K6KVFH5(Z5%\5(JGIMJG9K2RÚ8;OaK5~8UCQC25(49WFbZ7GI5qG6E=G6Fb:<FHZ7qWF8;7U4D8;:Õ
BAZ Nx%y z{TFaKJNK=%W G65EN8%ZNWOH=<8%Z_WFdc=Q4I=QZC2=%KFbZ~5(46:q8;GSN=QG=Q=QZGIE=GIFH:<FbZ7.KVJSÂ=`Ob=Q:<=`ZG
inputs
interface
outputs
operator
exist check
timing
initialization information
Fb7UJ4I=ho >X=QGD8%FbO5%GIE= !FH:<FbZ7?KVJSÂ=`Ob=Q:<=`ZG
8;ZWGIE=g5(MN=Q4D8%GIFH5(Z6@GIEFKFbZGI=`4V8(C]=TR;5(4=Q^8;:<MOH=TR%EN8;ZNWOb=%KGIE=XSJc=Q46FbZ7Y5;Ú8kKGI46=%8;: 5;5(4DWK5(4
8?SOb5CD5(46Fb=QZGI=LW5(MN=Q498;GI5U4Q
( )( / /*
!E=hGIFH:<FbZ7kKJS=QOb=`:<=QZG$4I=QM4I=%K=QZG9K!8kZ5%T=QOÍ8;MM4I5T8UCiEqG65f\W=%K6C24IFHMGIFH5(ZNK]R8%ZNW<!=M46=%KV=`ZGFbG
E=Q46=AFHZ7U4I=%8%GI=Q4cW=QG98;FbO"!E=G6Fb:<FHZ7hKJS=QOb=Q:.=QZGFbZC2ObJNW=%K$GIE46=Q=WFaKVG6FbZNC]GJZNC2G6Fb5UZNK2R8(K!FHZNWF CQ8;G6=%W
FbZ.FH7(J46=o >CQ8%OaC2JO8;G6FbZ7hGIE=AG6Fb:<FHZ7hWF 8;7(498;: 5;Ú8YC25(:<MN5UZ=QZG*@TCDE=%CDFHZ7G6EN8;GGIE=XFbZMJGDKFbZNW=`=%W
8;464IFHT=\\E=QZGIE=Q_§KVE5UJOaW@8%ZNW<C25UZG64I5UObObFHZ7G6E=A=`^FKVGI=`ZNC2=!5%G6E=A5UJGIMJG!U8;OHJ=%KKV5hG6EN8;GGIE=Q_Y5(ZOH_
I=`^F KVG \E=`Z<GIE=XGIFH:<FbZ7hWFa8%7(498;: KVMN=%C]F9CN=%KGIEN8%GGIE=Q_8%4I=U8%ObFaW 50C]5(ZGI4I5UON5;G6E==Q^FaKGI=QZC2=!5%GIE=
5(JGIMJG9KMN=Q46:<FbG9K!CDE=%CDFHZ7hGIE=hFHZMJG9KA8%G\GIE=5(OHOb5%\FbZ7C25(:<MN5UZ=QZGB7D
¥x Âz !Tzx ¢z¡!y zx
f!Ob=QT=`OFbZFHGIF8;ObFH%8;G6Fb5UZ8;ZNWG6=Q4I:.FbZN8%GIFb5UZC25(ZWFbG6Fb5(ZK5;Ú8YC25(:.M-5UZ=QZGQRT8UK\KVMN=%C2FdCN=%W?FbZGIE=gGIFb:.FbZ7
WF8;7(498;: 5;X8.C2Fb49C2JFbGgW8%GD8(KE=Q=QG`R8;46=?EN8;ZWOb=%WS_G6E=?GIFH:<FbZ7KVJS=QOH=Q:<=QZGQ !EFaKAFHZNC2OHJNW=%K\4I=%K=QG
KV=mJ=`ZNC2=%K8;ZNW<GI=`4I:<FHZN8;G6Fb5(Z%5Â= å7T=Q:.MG_FHZ7hSJc=Q4DK7D !E=hFbZFHGIFa8%ObFH%8;G6Fb5(Z.8;ZW G6=Q4I:.FbZN8%GIFb5UZFHZ5(46
:q8%GIFb5UZF KFHZNWFaC`8;GI=LW FbZÕFb7UJ4I=Ys<S_ G6E=WFH4I=%C2GXC]5(ZZ=LC2GIFH5(ZNKASN=QG=Q=QZqGIE=?x qKVJSÂ=`Ob=Q:<=`ZG
8;ZWGIE=YFbZMJG 5UJGIMJGQ!E=LKV=?C]5(ZZ=LC2GIFH5(ZNKXCQ8;464I_qFbZFbGIF8;OHFb%8%GIFb5UZ<FbZ5(4I: 8;GIFH5(Z"S-=`GV=Q=QZqGIE=kGIFH
:<FHZ7?KJS=QOb=Q:.=QZG9K5%8KV_KVG6=Q:~ !=LCQ8;JNK=hGIE=hSN=QEN8QFb5(4\5%8;Z"5(MN=Q498;GIFH5(Z"FaK\Z5(Gg8 c=%C2G6=%W<S_.GIE=
FbZFbGIF8;OHFb%8%GIFb5UZRTGIEFK!FbZ5U4I:q8%GIFH5(Z<F K!Z5(GXMN8(K6KV=%WqGI5GIE=Y y%zxL -yT
Azy%z ¢Tx%y;w
!E=hGIFH:<FbZ7?KVJSÂ=`Ob=Q:<=`ZG$FK\W=QT=QOH5(MN=%W4I5U: GIE=kK5;G\8%4I=hGI5T5UOaKXW=%K6C24IFHS-=LW FHZfålUoh0,A=Q4I=g!=h\FbOHO
dJNKG?7(FbT="8S46Fb=2gKJ:<:q8%4I_~5%hGIE=qMN8%4D8%:<=QGI=`4DK\EFaCDE¢KVMN=%C2F¹_GIE= G6Fb:<FHZ7!E=LKV=qMN8;498;:<=`GI=Q49K
\FbOHOSN=kJNK=%W FHZ G6E=?f \W=%K6C24IFHMGIFH5(Zq5;8KV_KVG6=Q:ÜFbZqGIE=5(OHOb5%\FbZ7KV=%C2G6Fb5UZN3$8;498;:<=`GI=Q49K!GI5GIE=
GIFH:<FbZ7<GI5T5UOaK?8;46=>GIE= '% 5;XGIE=<C25U:<MN5(Z=`ZG@ÖG6E=ZJ:SN=Q45%XFbZMJGk=QT=QZGDKXM-=`4kMN=Q4IFH5W'@
GIE=kZJ:SN=Q4\5%5(JG6MJGh=QT=QZGDK!MN=Q4MN=Q46Fb5W'@Í8;ZNWG6E=?ZJ:SN=Q4\5%\C]Ob5CDqC2_C2Ob=%K\FbZÕ8 ! !E=
'% 5;gGIE="C25U:<MN5(Z=QZGkFKkKM-=LC2F9CN=LWFHZ5(49W=Q4?G65~EN8;ZNWOb=qFbZFHGIF 8;ObFH%8;G6Fb5UZ8%ZNWGI=Q46:<FbZN8%GIFH5(Z6>
GIE=5UJGIMJGFKZ5(G§C25(ZNKFaW=`4I=%WU8;OHFaW~JZGIFbO ' % C2OH5CiÕC2_C]Ob=%K8QGI=Q4hG6E=FHZMJG8;4I46FbT=%K]R8;ZW
ObFHT=Q\FaK=GIE=?5(JG6MJGhC25UZG6FbZJ=%K\GI5<SN=Y(8%ObFW JZGIFHO$'% ¢C2_C2Ob=LK\8LGI=`4GIE=YFbZMJGAFKAZ5<OH5(Z7U=Q4
U8;OHFaWUBAObOC]5(:<MN5(Z=QZG9K8%4I=\MN=Q46Fb5WFC(R(8UK$W=Q: 8;ZNW=LWS_pm @(G6E= ! <FaKG6E=!ZJ:SN=Q45;ÍC2_C2Ob=LK
5; GIE=YKV_KVG6=Q: C2Ob5CD<MN=Q4\MN=Q4IFH5W 5%$G6E=h7(FbT=`ZC]5(:<MN5(Z=QZG`
! ¢ -x%zx Â
!E=?G6Fb:<FHZ7KVJSÂ=QOH=Q:<=QZG\:JNKVGXSN=?\4IFbG6GI=QZ"FbZ8<Oa8%Z7(J8;7(=.CQ8%MN8;SOH=?5;=Q^M4I=LKIKVFHZ7<G6E=?:<5(:.=QZG9K
\E=QZ8qKFb7(Z8;O$=Q^FaKGDKAFHZG6E=f\ K=QZNK=@-=?JNKV= !#" %'fåljhÚ5(4 -,g fål3h!E=?S-=`EN8QFH5(4QRN5(4
5(MN=Q498;G6Fb5(ZÍR5(Z~G6E=?5(G6E=Q4EN8%ZNW~CQ8%Z~S-=?\46FbG6GI=QZ"FbZ\E8;GI=`T=Q4AO 8;Z7UJN8;7U=FK:.5TKVGg8;MM4I5UM4IF 8;GI= @!=
G_MFaCQ8%ObOb_hJNK= f¹>QtjheZ?G6EFaK8%4IGIFC2Ob=\=A\FHObOM4I=%K=QZG C25(:<MN5UZ=QZGDKJNKFbZ7 !#"$&%$' 508hKV_ZNCDE4I5UZ5(JNK
W8%GD8 5; O 8;Z7UJN8;7U=7!5(4XGIE=G6Fb:<FHZ7?KJS=QOb=`:<=QZGQR8;ZNW 5U4GIE=5UMN=Q4D8%GIFb5UZKVJSÂ=QOH=Q:<=QZGQAFdc=Q
4I=`ZNC2=%K$FbZ.GIE=X4I=QM4I=%K=QZG98;G6Fb5(Z.5;ÚW8%GD8SN=QG=Q=QZGIE=G5?KVJSÂ=`Ob=Q:<=`ZG9KÖ5%GI=QZqC]4I=%8%GI=%KGIE=XZ=Q=%W?5(4
8;ZFbZGI=`4V8(C]=TR-G65q4I=Q5U4I7T8%ZFb`=W8;G98 MN8UKIKVFHZ7qSN=QG!=Q=QZ~G6E=?GIFH:<FbZ7<KJS=QOb=Q:.=QZGX8%ZNW~GIE=5(MN=Q498;GIFH5(
ZN8%O$KJS=QOb=Q:.=QZG@T!=hFb:<MOb=Q:=QZTGGIEFKFHZG6=Q4V8UC2=JNKFbZ7Oa8%Z7(J8;7(=LK4I5U: G6E=hG!5.KVJS=QOH=Q:<=QZGDK8(K
8;MM4I5UM4IF8;GI=
} =?Z5(GI=?G6EN8;GgGV_MF CQ8;OHOb_<G6E=?5(MN=Q498;GIFH5(ZRGIE=kJZC2GIFH5(Z~5;c8<C]5(:<MN5(Z=QZG`R-46=Q:q8%FbZNK\JZNCDEN8;Z7(=%W
4I=`7T8;49WOb=LKIK5%kG6E=~Ob=`T=QO\8%G \EFaCDE !="4I=Q7 8;49W G6E=G6Fb:<FHZ7B\G<8SOb5CD¢Ob=QT=QORG6E=~GIFH:<FbZ7KJS
=QOH=Q:<=QZGFKGI46FbFa8;ORQSJG$G6E=\5(MN=Q498;G6Fb5(ZKJS=QOb=`:<=QZG:JNKGSN=!JObOH_kW=QT=QOb5UMN=%WR%FbZk5U4DW=`4$GI5YKVJMMN5(4IG
KVFH:JOa8;G6Fb5UZTB\G!8?C]Fb4DC]JFbG60KM-=LC2F9CC\Ob=`T=QO0R%GIE=gGIFb:.FbZ7h=QOH=Q:<=QZG:JNKG46= N=%C]GG6E=G6Fb:<FHZ7YWFa8%7(4D8%: 5;
8?MN8;46GIFaC]JOa8%4XC2Fb49C2JFbG`RTM-=`4IEN8%MNKFHZNC2OHJNWFbZ7?8;Z"FbZGIF8;ObFH%8;G6Fb5UZq8;ZNW Q5(4XGI=`4I:<FHZN8;G6Fb5(Z KV= TJ=QZNC]=T
EN8;Z7(=%K\8%4I=X4I= TJFb46=%WkFbZGIE=AFHZG6=Q4V8UC2=X8(K!=QOHO0RT8UKGIE=AG6Fb:<FHZ7hCDEN8;Z7U=%K2RTG65M4I5(MN=Q46Ob_5(467T8;ZFbQ=
GIE=W8%GD8 _MF CQ8;OHOb_Y87U=QZ=Q46FaC!FbZGI=`4V8(C]=XKV=Q46T=%KGI5YC25UObOH=%C2G8YKVGI46=%8;:+5%W8%GD8hFbZGI5Y8;Z<FHZMJGSJ c=`4QR
8;ZWG65KV=QZW 8~KGI46=%8;: 5%hW8;GD8 465(: 8%Z¢5(JG6MJG?SJc=Q4`5(4?=Q^8;:<MOb=TRF¹XGIE=.GIFb:.FbZ7"WF8;7(498;:
KVMN=%C]F9CN=%KÚ8KGI46=%8;:+5%5(49WK!8%ZNW8hC2=`4IGD8%FbZ?O8;GI=`ZNC2_hSN=QG!=Q=QZ?G6E= CN49KVGFbZMJG8;ZWGIE= C4DKVG5UJGIMJGQR
8;ZW GIE=5UMN=Q4D8%GI5(4XFaK\8 KVJS4I5UJGIFHZ=h\EFaCDE<5(MN=Q498;G6=%K5UZ~8kSOH5Ci.5;Ú!5(49WK2R8;ZqFHZG6=Q4V8UC2=FaK!JKV=%W
GI5SJc=Q4\G6E=hFbZMJGXKVG64I=%8%:Ü8;ZNW"KVG65(4I=YGIE=h5UJGIMJGASOH5CiJZGIFHOFbGXKE5(JOaW SN=hGI498;ZNK:<FbG6GI=%W
!
. . !0
- /
e0ZGIEFaKkK=%C2G6Fb5(Z!= KVJ:<: 8;4IFHQ=kG55;XG6E=<G65T5(OaKk\EFaCDE EN8QT=<M4I5%T=QZJNKV=2JO5(4§W=%KFb7(ZFbZ7"GIE=
GIFH:<FbZ7?KVJSÂ=`Ob=Q:<=`ZG8;ZW FbZGI=`4V8(C]=Ob5U7(FaCURN8;ZNWq=Q^MOa8;FHZ<E5% G6E=Q_<46=QOa8%GI=hGI5.8 _ZNCDE465(Z5UJNKAg8;GD8
OH5;*7(498;MEÍN5U4X8p:.5(4I=gW=QG98;FHOb=%W=`^MO8;ZN8%GIFH5(Zq5;G6E=G65T5(OaK]R-G6E=h4I=%8UW=Q4FaK!4I=]=Q4I46=%WGI5%fl(oh !E=
GI5T5UOaKkM46=%KV=`ZG6=%WE=Q46=\FHObOSN=<JNKV=LW FbZ 8;Z=`^8%:<MOb=Y5;gK_KGI=Q:<Ob=`T=QO$K_ZCiE465(ZFH%8;G6Fb5UZ FHZ8qOa8;G6=Q4
KV=LC2GIFH5(Z
-1 1
H process
information
READ WRITE
H_IN H_OUT
initialization
Fb7(J4I=Yt> !E=q3$4I5C2=LKIK
dependency
Clock System H_OUT WRITE READ H_IN
Fb7UJ4I=>$T=QZGDK8(K6KV5C2F 8;GI=LW\FbGIE
!E=M465C2=%K6K?KVE5%\Z FHZ Fb7UJ4I=qt~FaKhGIE="KFb:<MOH=%KVGh5%G6E=qGIFb:.FbZ7qM465C2=%KIK=%K2e0GC25UZG98;FHZNKkG!5
C25UJZG6=Q4DK]RQGI5gC25(JZGFbZMJG8;ZNWk5UJGIMJG=`T=QZG9K2R`8;ZNWY8AW=`Oa8Q_ObFHZ=$5(4GIE=FHZFbG6Fa8;G6Fb5UZk8%ZNWkGI=`4I:<FHZN8;G6Fb5(Z
C25UZNKVFW=Q4D8%GIFH5(ZNK]$e0ZGIE=qCQ8(K=<5;gK5(:<=q*Z5W=%K]R$\FbGIE 5(Z=<SOb5CD 5%XFbZMJG?8;ZW5UZ=<SOH5Ci5;
5(JGIMJG`RG6EFaKhGIFb:.FbZ7<G65T5(O\F KkKVJ 8qC2FH=QZGGI5W=LKIC246FbSN=G6E=qK_ZNCDE465(ZFH%8;G6Fb5(Z 5;g8 Z5W=@5UGIE=`4I\FaK=TR
5(G6E=Q4\G65T5(OaKgKVJNCDE"8(K!GIE=.M4I5C2=LKIKX8;4I=hZ=`=%W=%W
BAObOKVFH7(ZN8%OaK 50W=QZ5(G6=%W?S_§8;4I465%XK FHZFb7UJ4I=Xt7Ú8;4I=XSN5T5(OH=%8;ZR8%ZNWK_ZCiE465(Z5UJNK\FHGIE8hC25U:<:<5(Z
C2OH5Ci(}E=QZ=QT=Q4 % F KGI46J=TRTGIE=Q4I=XFaK8;Z.FbZMJG!=QT=QZGQR 8;ZNW\E=QZ=QT=Q4 ! FaKGI46J=TRTGIE=`4I=XFaK
8;Zq5UJGIMJG\=QT=QZGQTe0ZMJG!M465C2=%KIKFbZ7KGD8%4IGDK!\E=QZ !#~S-=LC25(:<=LK G64IJ= R8;ZW CNZFKVE=%K!\E=QZ !#~FaK
8;O KV=T !E=KFb7UZN8;O q7(5T=%KGI4IJ=\\E=QZGIE=X5(JG6MJGKVG98;46GDKSN=QFHZ7hU8;ObFWR(Få=TU8LG6=Q4GIE=XOa8%GI=QZNC]_k5;
GIE=kC]5(:<MN5(Z=QZG\E8(K\MN8(K6KV=%WÎ3$8;498;:<=`GI=Q49KGI5GIEFaK!M465C2=%KIKX8;46=>GIE='% SN=QG!=`=QZ<FbZMJGX8;ZW
5(JGIMJG@G6E=ZJ:SN=Q45;XFHZMJGh=QT=`ZG9K 'MN=Q4kMN=Q46Fb5W'@GIE=<ZJ:SN=Q4X5;X5UJGIMJGk=QT=QZGDK '
MN=Q4MN=Q46Fb5W'@8;ZNWG6E=kZJ:SN=Q4\5;C]Ob5CDC]_C2OH=%K!FbZÕ8 ! Ne0ZÕFb7UJ4I= TRN!=?KE5% GIE=?FHZNKVG98;ZGDK
8;GX\EFCiE<G6E=h5(JG6MJG9KA8%4I=kG64IJ= R7(FHT=QZq8%Z<M465C2=%K6K T
-1 1
!E= M4I5C2=%K6K<KVE5;\Z FbZ Fb7UJ4I=Õn FKpJNK=%W G654I=LKV_ZNCiE4I5(ZFbQ=<U8%ObJ=%K]RG6E=~K_ZCiE465(ZFH%8;G6Fb5UZ 5;
\EF CiE*W=`M-=`ZNWK 5UZ G6E= KV_KVGI=`:~R498;G6E=Q4qGIEN8%Z dJNKG8¢KFbZ7UOb= C25(:<MN5UZ=QZGQeGqF K JKV=%WGI5U7(=QG6E=Q4
\FbG6EG6E=kFHZG6=Q4V8UC2=hOb5(7UFaC(RG65<SJc=Q48;ZNWqJMKI8;:.MOb=Y(8%ObJ=LK2eG\FKAMN8%4IGIF C2JO 8;4IOH_<JNK=2JO5(4gC25(ZGI465(O
SLOW R process
FAST WRITE
Fb7(J4I=Yn> !E=q3$4I5C2=LKIK
System Clock WRITE SLOW
FAST
dependency
Fb7UJ4I=Yr>$T=QZGDK8(K6KV5C2F 8;GI=LW\FbGIE
U8;OHJ=%K\EFCiE§8;464IFbT=Ob=%K6KÖ4I=mJ=`ZG6Ob_G6EN8;ZW8%GD8R(SJG$:JNKGZ=`T=Q4IG6E=QOb=LKIKSN=\M4I=LKV=QZG 508%ZNWkM465(MN=Q4IOH_
KV_ZNCDE4I5UZFb`=%W7$=L8(CDE G6Fb:<=XGIE=5UMN=Q4D8%GIFb5UZ~KJS4I5UJGIFHZ=kFK\CQ8;OHOb=%W
BKA\FHGIE~GIE= M4I5C2=%K6K2R8%ObOÚKVFH7(ZN8%OaKh8;46=KV_ZNCiE4I5(Z5(JNKA\FHGIE8<C]5(:<:<5UZ"C2Ob5CD !E=YFbZNC25U:<FbZ7
U8;OHJ=%K\8;464IFHT=k8%GAG6E=hFbZMJG
' ~ !E=Q_q8;46=kG64D8;ZK=Q464I=%W<GI5GIE=5UJGIMJG %
~\E=QZ=QT=`4 !
FaKGI4IJ=TR!8QGI=Q4.8¢KVMN=%C2FdCN=%W¢Oa8;G6=QZNC2_ !EFaKM4I5C2=%K6K<FaK8;OaK5¢M-=`4IFb5WFaC(RGI5SN=~JNK=%W GI5U7(=QG6E=Q4<\FHGIE
MN=Q4IFH5WFaC.C25(:<MN5UZ=QZGDK23$8%4D8%:<=QGI=`4DKGI5~G6EFaKhM4I5C2=LKIKk8%4I=qGIE=qKI8%:<=<8UKkGIE5 KV=5U4?GIE= M465C2=%K6KB>
GIE='% SN=QG!=Q=QZ"FbZMJG8%ZNW5(JGIMJG@-G6E=?ZJ:SN=Q45;FbZMJGX=QT=QZGDK '¢MN=Q4MN=Q4IFH5W'@NGIE=
ZJ:SN=Q45;Ú5(JG6MJG=`T=QZG9K ' MN=Q4XM-=`4IFb5W@N8;ZNWG6E=hZJ:SN=Q45;C]Ob5CDqC2_C2Ob=%KFbZ"8 ! e0Z
FH7(J46=\rRU!=\KE5% G6E=!FHZNKVG98;ZGDK$8%G$\EFaCDEkG6E=\5(JGIMJG9K$8;46=\GI46J=TR%7(FbT=`Z?8;Z YM4I5C]=%KIK T
$ . . # )" ! &
XJ4h8%SNKVG64D8(C]G:<5W=QOOH=%8(WKAGI5q8(8%4IFH=QG_ 5%c8;MMOHFaCQ8%GIFH5(ZKVMN=%C2FdCC 55(4hKFb:JOa8%GIFH5(ZKVMN=%C2FdCCj7ÚFb:<MOH=Q
:<=QZGD8%GIFH5(ZNK]RW=`M-=`ZNWFbZ7 5UZGIE=W=%KVFH4I=%W~4I=LKVJOHGDK2ÍBK:<=QZGIFb5UZ=%Wq=%8;46ObFb=`4QRWF9c=Q46=QZGKVJS=QOH=Q:<=QZGDK
8;46=A\46FbG6GI=QZ?FHZ8U8%4IFb=`GV_Y5;ÍOa8;Z7(JN8%7(=%K+> G65kKFb:JOa8%GI=cC25(:<MOb=Q^ eÍJZNC2GIFH5(ZN8%ONSOb5CDK+@!#"$&%$'
GI5.8;OHOb5% 5U4I:q8%OT=Q46F9CCQ8%GIFH5(Z6@8;ZNW -,g G65<MN=Q4I:.FbG\K_ZGIE=%KVFK!5;C25UZG64I5UOKVGI46JNC2G6J4I=%K!5(4g8;Z"Fb:<
MOH=Q:<=QZGD8%GIFb5UZeGYFaKh=%KIK=QZG6Fa8%O 5U4CiE=%CiFbZ7<GIE= KV_ZNCiE4I5(ZFb%8%GIFb5UZ G6EN8;G?G6E=<G6Fb:<FHZ7qKVJSÂ=`Ob=Q:<=`ZG
SN=\46FbG6GI=QZ~FHZ8Oa8%Z7(JN8%7(=qC`8;MN8%SOb=?5%\4I=`M4I=%K=QZGIFbZ7<GI=Q:.M-5U4D8%O$C25UZNKVG64D8%FbZGDK2 !E=5UMN=Q4D8%GIFb5UZKJS
=QOH=Q:<=QZGQRI5UZkG6E=5(GIE=Q4E8;ZNWRUCQ8%ZkSN=\4IFbG6GI=QZhFHZ\E8;GI=`T=Q4Oa8%Z7(JN8%7(=\SN=%KG=Q^M46=%KIK=%KGIE=<58;SNKGI4D8UC2GB7
5(MN=Q498;G6Fb5(Z"GI5SN=MN=Q45(46:<=%W
e0Z~GIEFKKV=%C]GIFb5UZRN!=?M46=%KV=QZGXGIE46=Q=WF9c=Q46=QZG6GI=%CDEZ5UOb5(7UFb=%K p5(4gFb:<MOH=Q:=QZG6F¹Z7C25(:.M-5UZ=QZGDK]R
Ob=L8(WFHZ7kG65kGIE4I=Q=gWF9c=Q46=QZGJKV=%K5;GIE=ObFHS4D8%4I_T"!E=ObFHS4D8%4IFb=LKKEN8;46=GIE=hKI8%:<=C]5(:<MN5(Z=QZG:<5W=QO0R
GIE=<K68;:<=8%SNKVG64D8(C]G5UMN=Q4D8%GIFb5UZNK2RÚ8;ZNW~GIE=<K68;:<=?MN8%4D8%:<=QGI=`4DK2e0GhFaKh8;O KV5qFbZGI=Q46=%KVG6FbZ7.GI5qZ5(G6=G6EN8;G
8;OHOAG6E4I=`=ObFHS4D8%4IFH=%K?KVEN8%4I=~G6E=~K68;:<=q5(MN=Q498;G6Fb5(Z*KJS=QOb=`:<=QZGDK2R\4IFHGIGI=`Z FbZ \EF CiE :q8;T=LK5(4
4I=L8(KV5UZN8;SOb_<8(KGKFb:JOa8%GIFb5UZNK2
B¢KVFb:.MOb=$OHFbS498;46_5;C]5(:<MN5(Z=QZG9K-\46FbGIG6=QZk\FHGIE !#"$&%$'g8;ZNW 8%ObOb5%XK8!JZNC2G6Fb5UZN8;OKVFH:JO 8;G6Fb5(Z
5;8qKV_KVGI=`: 8;GhSN5(G6E8%Z8%SNKVG64D8UC2G?8%ZNW 8qC25U:<MN5(Z=`ZG60KM-=LC2F9CChOb=QT=`O0 !EFKMN=Q46:<FbG9KG6E=W=%KFb7UZ=Q4
GI5?=`^MN=Q46Fb:<=QZG\FbGIE"8k7UFbT=QZ.C25(Z CN7(J498;G6Fb5(ZÍRN8(K!FbZ $'! +8%ZNW<GI5?G6E=QZqW=LKIC2=QZWGI58?C2FH4DC2JFbGI
KVMN=%C]F9CCKVFH:JO8;G6Fb5(Z\FbG6E5(JG?CDEN8;Z7UFbZ7~G6E=.C25(ZC7(J498;GIFH5(Z$}=<M46=%KV=`ZGYGIE=.KVMN=%C2FdCCQKh5;KVJNCDE8
ObFHS4D8%4I_<FHZ<GIE= C4DKVGX5; GIE=5(OHOb5%\FbZ7?KVJSNKV=%C]GIFb5UZNK2
B ObFHS4D8%4I_5;gC25U:<MN5(Z=`ZG9K\FbG6EGIFH:<FbZ7KJS=QOb=`:<=QZGDKA\46FbGIG6=QZJNKFbZ7~G6E= !#" %'!XKVJSNK=QG?5;
!#"$&%$'8;OHOb5%XKG6E=hJNKV=g5; 85(4I: 8;OT=`4IF9C-CQ8;G6Fb5(ZGI5T5UOGI5?T=Q46F_?G6E=M465(MN=Q4XKV_ZNCDE4I5UZFbL8;GIFH5(Zq5;Ú8
KV_KVG6=Q:~ !E=\T=Q46F9CCQ8%GIFH5(ZkFK$M-=`4V5(46:<=%WhJNKVFHZ7 Ö=Q46ZN8;46_A=%C2FKVFH5(ZAF8;7(498;:qKWfårjhR(\EFCiE§8;4I=gKVFH:<FbO8;4
GI5 !FbZ8;4I_.A=%C]FaKVFH5(Z"AF8;7(498;:qKlfojh !EFKFK!M4I=%K=QZGI=%WFHZqGIE=YKV=LC25(ZNWqKJSNKV=LC2GIFH5(Z
B OHFbS498;46_ 5;pC25(:.M-5UZ=QZGDK\46FbG6GI=QZJNKFbZ7 -, 5c=`4DK G5 8UWU8;ZGD8%7(=%K+>AGIE= CN4DKG FK<GIE=
FbZC24I=%8UKV=%WkMN5 KIKVFHSFbOHFbG6Fb=%KÖ5U4=Q^CDEN8%Z7(=XJNKVFHZ7hGIEFK$ObFbZ7(JN8A4D8%ZNCQ85;ÍEN8;49W\8%4I=hW=%KVFH7(Z6@(G6E=gKV=%C25UZNW?FaK
GIE=kMN5TK6KVFbSFbObFHG_5%!=`T=QZG6JN8;OÍ8;JG65(:q8%GIF CK_ZGIE=%KVFK!5;FHZG6=Q4V8UC2= I7(OHJ= ?Ob5U7(FaCA465(:ÜGIE=§KVFH:JO8;G6Fb5(Z
:<5W=`O0 !E= ,SN8(K=%W OHFbS498;4I_FaK!M4I=%K=QZG6=%W<FbZqGIE=G6EFb49W<KVJSNKV=%C]GIFb5UZ
+1&( 2( + * (#/ ' ( ,+
e0Z~GIEFKAKJSNK=%C2GIFH5(Z~=kM46=%KV=QZGh8S8(KVFCOHFbS498;4I_"5;cC25U:<MN5(Z=QZGDK]R\EFaCDEMN=Q46:<FbG9K5UZ=?GI5.M-=`4V5(46:
KVFH:JOa8;G6Fb5UZNK5%YKV_ZNCDE4I5UZ5(JNKW8%GD8;2N5% KV_KVG6=Q:qK2Úe0G8;OaK5KJMMN5(46GDKG6E==`T5(ObJGIFb5UZ5;8 W=LKVFb7UZR
KVG98;46GIFbZ7\FHGIE"8pSOb5CDOb=QT=`O:<5W=QOÍ8(K\FbZqGIE=G64D8UWFbG6Fb5(Z8;O$T_ZNCDE4I5UZ5(JNKX8%GD8Ob5%hRN8;ZW :.5;FbZ7
GI5%c8;4DWK8gKV_KVGI=`:C]5(:<MN5TK=%Wk5;ÍC2FH4DC2JFbG:<5W=QO K2 !EFKSN8(KFaC!OHFbS498;4I_h5c=`4DK$GIE=X8UWU8;ZGD8%7(=%K$G_MFaCQ8%O
GI5§8kEFb7UEOb=QT=QOOa8;Z7(JN8%7(=>FHZ5(46:q8;G6Fb5(ZEF WFbZ7 5ÂFHZG6EFaKCQ8(K=GIE=KVMN=%C2FdCCQK5%E5%=%8(CDE<5UM-=`4D8;G6Fb5UZ
FaK<FH:<MOb=`:=QZGI=`W7?@$:<5WJO8;4IFHG_TRFH:<MN5TK=%W S_G6E= C25(:<MN5UZ=QZG<:<5W=QO @\8;ZW :q8;FHZG98;FHZN8;SFHObFHGV_UR8(K
GIFH:<FbZ7<WF 8;7U4D8;: K8;ZNWJZNC]GIFb5UZN8;OHFbG_~8%4I=?FHZNW=QMN=QZNW=QZGg5;\G6E=C2FH4DC2JFHGAFH:<MOH=Q:<=]ZG98;GIFH5(ZR8;ZNW CQ8;Z
SN=hJMW8;G6=%WK=QMN8;498;G6=QOb_q8UKAC]5(:<MN5(Z=QZG9K!=QT5(OHT=T
! { ! ! ¡ !
!E=XSOb5CDÂOH=QT=QO:<5W=QOFaK$FbZKVMFH4I=%WkS_?GIE=hW5U:q8;FHZ?5;3$G65(Ob=`:_TRU8;ZWpS_?GIE=XSOH5Ci§WFa8%7(4D8%:qK
\EF CiEK=Q=Q:ÜFbZGIJFHGIFHT=G65q:<5TKGhW=%KFb7(Z=Q4DK]!E=:<5W=`O:q8%T=%K\FbG=%8UKV_"GI5"W=%KFb7(Z8<G64IFa8%OKV_KVG6=Q:~R
8(KhGIE=C]5(:<MN5(Z=QZG9Kh8;4I=.C2OH5TKV=?G65G6E=8;SNKGI498(C2GY5(MN=Q4D8%GIFH5(ZNKh\EFaCDE~GIE=`_~Fb:<MOH=Q:=QZG` !E=:<5W=`O
8;OKV5<: 8;T=%K5U44I=%8UKV5UZN8;SOH=KVFH:JO 8;G6Fb5(Z.GIFb:.=%K2R8(K8%ObO:q8;G6E=Q:q8%GIFaC`8;O8%ZNW~C25UZG64I5(O5(MN=Q498;G6Fb5(ZK8%4I=
MN=Q4V5U4I:<=LWS_ KVJS465(JG6FbZ=YCQ8%ObOK!!5(46FHZ7WFH4I=%C2G6Ob_5(ZqSOH5CiK!5;W8;GD8
e0Z¢8SOb5CDÂOH=QT=QOC25U:<MN5(Z=`ZG`RÖG6E=qGIFH:<FbZ7 KVJS=QOH=Q:<=QZGFaKkG_MFaC`8;ObOH_G64IFbFa8%O0RC25UZNKVFKVGIFHZ7~5;g8
KVMN=%C]F9CCQ8%GIFH5(ZG6EN8;Gg8;OHOFHZMJG9KA8%4I46FbT=Y8;GXGIE=§KI8%:<=hGIFb:.=TR8%ZNW G6E=k46=%KVJOHGAFK\8Q(8%FbO8;SOH=?8LG6=Q4g8pJZFbG
W=QO8Q_T!E=5(MN=Q498;GIFH5(Z KVJSÂ=`Ob=Q:<=`ZG`R5(ZG6E=5UGIE=`4E8;ZNWR:JKVGSN=?JObOH_W=QT=QOH5(MN=%WFbZ5(49W=Q4hGI5
MN=Q4V5U4I:Ü8?KFb:JOa8%GIFH5(Ze0ZG6=Q4V8UC2= I7(OHJ= kOH5(7(F CFaK!G_MFaCQ8%ObOb_YObFH:<FbG6=%WkGI58?SJc=Q4\JNK=%W<GI5KGI5(46=hGIE=
4I=LKVJOHGA5%\GIE=k5(MN=Q498;G6Fb5(Z~5(48 JZFbGgW=QO 8L_ BAZ~=`^8%:<MOb=g5;X8SOb5CDOb=`T=QOC25U:<MN5(Z=`ZGXFaKA7UFbT=QZ"FbZ
GIE=5UObOH5;\FHZ7KV=LC2GIFH5(Z