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Unformatted text preview: © © 'D C AB @ 9 3 ! ¥   ¨ £       § ©£ ¦  §¨ ©   ¡ §  ¡   §¦ ¡   ¦ " § ¦ § ¡  ¥¦ ¥ §£ ¥ §£  § ¤ §¨ £ § 8 £ § 8 ¦ ©  5'4  ¢ § ¡ & 10   §  ©£  # 8 7 % 33 6 20      §£ ! §£   ¡ ¦    © © © ¨ §¦ ¡ ¡ § ¥ ¤¥ £ ©£  £ ¢  ©   ¡  ¥ © ¤¥ ) 13 20 # ) '( $& &'% $ 7 C ' @AB c 9 h c 3 b fq h dt p r cf i ` z dv t dv t XY –• n u p q n• du c f s V ‰w ƒ l he i ~ x7 m ix o Dn { bq f rt rc d —• – ‘’‚ UT } “” t e ds H t p” t t ds W hf c V p b s FE S ‰ i i fh t s r ˆ e pe H i QR t h r i ƒ w fh gei” †‡ u x y– t j k– ‚ dc H p f ‰w €† rc F q QP ƒ c e t ‰ “” y dv t u ds j– d —• – … x„ p ih € cg yh h s f p 8 8 ‚c dc e ˜– ™—• r i | f v” ut “” p f t c{ 7 5'4 eq D j f se ” % 3 3 6 20 € } } { ‰w i f w xs & 10 r i z ) r c dc i e dc r 13 20 e bc r tf br r i 8 h r r ‚ e GHI c EF d rt b cf f d ds e ce dc t vp ab ) '( p $& &'% $ y | C ' AB @ 9 3 dt p cf z ˆ ‰‚ h i c d z f i e if v| vi ds c{ z – r cf e bc h ‰ u rc –d „ s c x ‡– t ‰ w r i ˜– „ x7 j …– ‹{ ‰ 8 8 h 8 7 r D c{ e– t p f % 3 3 6 20 iŠ h † ‰w t 5'4 t & u ds h 10 j …– „ c } p f c ‰ ‰w dc ‰ i ) 13 20 t ) '( ds br $& v &'% $ l f e n c p c r f t c c ih dc z h b r b e t c u '“ rt i gh s 8 8 8 % w 3 }r 3 6 20 5'4 te f & i t 10 cf f h } C @AB hf } h h d ce ‘ f t h }x t u e rt ‰ 7 r e s b h c z h i rc i f de bt f c b ‰ dc q t 7 g v  c g t rt s } dc f wh e f b w xs he d 3 x| { { ’D { z q c ‰e c p t } c br c dv t f rc h u dc f wh c h c d r c rc s f t u rc i ‰e cf } w rŒ h he d 7 i ce c{ z c b e f c i f f f ) 320 1 f f ) '( t e vp Ž b f 9 p wh rt ih dc r xh dt i if ˆ b i rŒ c h c ‰ b f D c{ h r iŠ h } c u n hg c p ‰ e jn cf iŠ ‰ e s bc z ƒw t f  x| vi ds de ‹{ n b h m o Dn f t wx †d ft c f ˜† f ‰ ƒw h s r c vh ‰ ˆ en t de u n j e c dc bc e br b $& b f &'% $ UT } H t ¡ C ' 9 3 ‰ c r v c f q w ‰ r t i e p f t u d Ÿ Œd t r e eh bc e r } ‰ c p } } } dc dt c r c ‰ e f r rt ž ˆ h ’ dc p f }w e rt  w p i t u xq f p cf r r i ce r dc 8 b rt f 8 cf p f p e df g t f tw r  d s e 5'4 & e de 10 xc v r w rc dt ) r i p  b b t if vp 8 7 ‰ % 3 3 6 20 r rt s e i } i pf e e f v @AB h i h ab b t ’ ˆ } } e c h r s xh v r g c S er rt QR bc c H ž EF } H F QP r dc vi h }v ih ‰e it rt GHI h ` EF w c r Y š G › œV T e ‰w t ™ ds — rt dt i ˜ s if cf z PF— ˆ ‰‚ – d GH i rt e r ih F• H d ” tw v vi ‰ Žr 13 20 ) '( e e r v $& v &'% $ ‹ ¥ ­ C ' AB @ 9 ‚ 3 i d f dt e ¥ h t dt h h v g v wh rf i x c h © c ¤¥ p p t ds ª b if dt } § ¨Ÿ i }e t { e b d cf } b e x s i h } bc f w ¦ ~ r vc † i } v ˆ fh b p e © ª x t e e c d f 8 8 ‚t ‰g ih % 3 3 6 20 c 5'4 h h rt & p c h h wh 10 wp rt v g £ i‰ i ¢ 8 7 « ¬ f dc c ‰ p t d f e w h } ‰ r i ¦ ~ ˆ §Ÿ cg dt b h h uc r  ˆ} dc r h u ˆ q i d f ‰ i f r if ˆ e df ž s w c c{ q } c d j f t u }v if h bc br t c p } v ‰ e it rt e dt v f ‹{ e ’ ˆ ¤ d e h vi h p i ce xh e vh ˆ pw ¢u ¦ ~ s ‹ ¤ † ‰ r ce w f } ds ˆ dc w h vh h £ ¢ ) 13 20 ¢ ) '( $& &'% $ c dt u® b ¶ C ' AB @ c 9 dc 3 br f | t j¤ u ¯ c rt ~ i f d ¯ vh µ ´ 7 w µ ~ ´ w e h r cf d ce ¯ c v} u D ³ j s x j† p vi b ~ 7 ~ w b p ~ wD e t rt p | w dv t t e ds r uc s ‰e c dc e ‰ fh f ih ‰w ds c ² b p f ‰w ~ dc g r t ds f p wt e c }x } ± ±~ ± 7 ~ 8 8 8 7 °u f tw ° % u 3 3 6 20 5'4 ~ j s ¯ p d & 10 t }Œ v r | D ° u dc p Œt v b if dt ‰g q } ‚ ce ‰ e he i he ) '( ab tw f ) 320 1 cg d ab $& &'% $ b p · 9 r 3 i h c bc e vc t b f t p yh u t r t c he b  f r i z t b if v x‰ c p ³ d ~ b ‚ } i | es d f w f  } e 7 xc t z } } v ~ w x t g wh 8 8 7 % h eh vc c 3 3 6 20 i t t u 5'4 & p 10 b v~¦ r w 8 e r iq h i eh dt ~ v t wD t f z b h t ‰ if f c e µ ~j ‰ e t † ¢ f C ' @AB ‰ c iŠ dc t p f f r de pe d b h i }Œ p f d g ‰w t ds he c dc de d f tw r ce c p t }Œ cf cg b b u f rt bc rt i i f f e r cf ² r v c }v f s ´ c vi c b ab i br d ¢ ) 320 1 ¢u ) '( $& g &'% $ c h bc ~ µ ´ ~ t i t p } C C ' 9 3 e t t f rt i h f v w r ig d de i dt p c f v d c cf p w xs r xr t d t r c 8 t b t ih c d d 8 f i bc ‰ v % 3 3 h 6 20 h c 5'4 p & t c i 8 7 r ‰f h c h  } dt c c r cf d w xs p c c q ¯ c f b f if ab c xh z c } s t z r tf tf r i dt f b h he c if f c r i h vp i ‰ t u d t f~ r ih t t }Œ r s t d p b b hf c hf ¸ e vh b e f~ fq i rt žw u i s i r p b he c wp e 10 ds ut h f c v} u c r i p ) '( f $& u g f ) 320 1 b t r b @AB ¦ ut u d rt f f b w r vc b b t u u c vc cg h f dt ¸ eˆ e c vc h f b c r i ¯ vc dv c c b c f ‰ r cf b f r w x rt d tf rt i t f f d e v r cf e f ‰ e c s t }Œ b f t if e vp ab vi &'% $ b p ¹e 8 C 'D A @B 9 3 ys c h f c }x s 7 p ¯ b c D u rt t u df s e s e ˆ ³ | 7 wD ³ | | | w w 7 7 7 7 wD f e ¸ r c w w | D w ² ² t ² 7 | 8 7 t | w 7 D wD i vc } | ¯ t u df s e p ˆ ³ ‰w s ¯ t e v ‚ ce df h d f wt ˆ t dt ds uh c ‚ i h d f dt vq e D r } d b fh | D 8 8 D 7 uc ƒuy e b b ’uy hf uy ® r r c t d t d f w xs t s 5'4 d h h bc & h bc º 10 bc º ¢ % 3 3 6 20 r t v b if dt q } xƒ vp ce c r t ab º ¢ ) 13 20 ¢ ) '( ‘ f d $& &'% $ s 7 ¯ ¯ t u u DC 'D @AB 9 D t u df s e s e ˆ ³ ˆ ³ | ³ | | | w wD 7 7 | w wD | D w D wD ² ² | ’uy 8 | 8 8 7 uy ® r % 33 6 20 r t d d t bc bc 5'4 d h h ¢ 3 | ¯ t df df s e ˆ 7 w 7 7 w 7 D w ² 7 7 D D ƒuy r t º º x’ c & h 10 bc º ¢ ) 320 1 ¢ ) '( ‘ f $& &'% $ s | ¯ ¯ t D u u 7 C 'D @AB 9 t u df s e s e ˆ ³ ˆ ³ ³ | 7 wD | w 7 | 7 7 wD w D D wD w ² ² 8 | 8 8 7 ’uy uy ® r % 33 6 20 r t d d t bc bc 5'4 d h h ¢ 3 7 ¯ t df df s e ˆ | | w 7 w 7 | D w ² 7 | 7 D D ƒuy r t º º x® c & h 10 bc º ¢ ) 320 1 ¢ ) '( ‘ f $& &'% $ A 13 B 11 B ¼» B 32 22 12 ¿ A 12 B 21 ½¾ A A 11 11 A 23 A 11 32 22 12 32 22 12 A 22 B A 21 B 11 B B B 21 B B 31 B 31 B A 33 A 33 B 11 A 32 A 11 A 22 A 11 A A 11 11 B B A 31 * B 31 B 21 A 22 A 33 A 22 A 33 A 22 A 33 B B 13 23 33 33 23 13 33 23 13 B B B B B B B Starting Positions Broadcast blocks of A within each row Multiply local blocks (not a global matrix multiply) $ &'% $& '( 3 ) 13 20 10 & 5'4 6 20 3 % 7 8 8 8 3 @B 9 A 'D | C ) A 13 B 11 B B 31 B B 32 22 12 À A 12 ½¾ A 11 B 21 B ¼» B B 31 B B 21 A 33 B 11 B 12 32 22 12 32 22 B 21 A 23 A 32 A 12 B B A 22 * B 11 B 31 A 21 A 31 A 12 A 23 A 12 A 31 A 12 A 23 A 31 A 23 A 31 A 23 A 31 B B 13 23 33 13 33 23 13 33 23 B B B B B B B Roll block rows of B up one mesh row with wraparound Broadcast blocks of A within each row Multiply local blocks (not a global matrix multiply) $ &'% $& '( 'D 3 ) 13 20 10 & 5'4 6 20 3 % 7 8 8 8 3 @B 9 A “C ) A 12 A 13 32 22 Á B B ½¾ B 31 B 21 ¼» A 23 B A 22 B A 21 B 31 B 12 B 11 B B 11 B 21 B A 33 A 13 B 31 B A 32 A 13 B 11 B 22 12 32 22 12 32 A 13 A 21 B 21 A 21 A 13 A 21 A 32 A 32 A 21 A 32 A 31 A 11 * A 32 B B B B B 23 33 13 33 13 23 33 B B B 23 13 B C is complete and in place after this step. One more roll restores B to its initial location. Roll block rows of B up one mesh row with wraparound Broadcast blocks of A within each row Multiply local blocks (not a global matrix multiply) $ &'% $& '( 3 ) 13 20 10 & 5'4 6 20 3 % 7 8 8 8 3 @B 9 A 'D ¡ C ) ‰ r h c rt i he c ­ C 'D A ˆ 9 e i} ˆ h s dc i } f u‰ d e d v i c @B 3 p b p pf e h bc dt v h f iq c w c } wq w r d ‚ x‰ i c }x t d u e d d ‰ w dt f c c s g v t r } p } dt e v  8 dt 8 % 6 20 p 5'4 te } c cf 8 7 c v r 3 3 } v ce f e p dt b d u & 10 ‰ dc t f   Ãc d ce c h b i g ip p b vc du c b s eh i rt } h f  p te }  b f e i c p te } c v c } v p iŠ h xh d g i £ b ¢ r cf  f pe d cf dv t f d e t tf ‰f c c f d s f ie ‰ e d ce w vi h ce h v ih g } r p e e r ce v b if dt q } p p b t }Œ i ce d ce f e ab v ¢ r b ) 320 1 e f ¢ ) '( $& &'% $ x‰ c f e b h ‰ r x rc e f rt c f f v } q b c ¶ C 'D A 9 f t r b u b rt hf i q c pf wh r e i‰  h  i ip r c rq he f ce 3 c ‰ b ‰f e f t u ce u e r rt q i pf ce s h ih dc c ‰ ‰ rt i r  w t v dc f e f w xs if b dt }e q } p t vp Æ ‰e e t w xs r h }x  8 8 cf i 7 d t i‰ f p % 3 3 r e 8 p rt r i ce } s f wh c Æ i 6 20 v e 5'4 v e b f dv t rc du c s & if ‰ e dt c du c f uÈ Ç ¢ @B q r i dc e e ih b } t b if c dt r c c f v p iŠ h e cg if dt ip b p c f rc }Œ s h i f f c ds s h c cg rt i d e  ip c t vp p f t f e v ¢ d dv t i c gq } ‰ iz x ‰ t c c if h dt b rt q e b z b if t dt e bs i r c pf ce b f f v rc s h cf dv c q } u rt s h de pf f ie ds e gq dt p ¸ ce b c d t ‰ r ˆ pe v‰ c c r dt h ‰ e p c Ž d ¢ rt de ui s r cf h f i‰ Å xh e  ip b c f t h u b u iq v i w c f } tg v e f f ‰ e v c b if dt q } } h r i e u ‰ i rt i d p f c } e w d f ce b fh vh cf }e h cf rc f z pe i bÄ b e bs t yc dc dt c f dv t b‰ c c up h i w w de p b gq } t e ds s e e f b t d ce t rc q c ¢ 10 q } b ) 320 1 e f ¢ ) '( ab $& &'% $ ‰ r } } rt } eh r i ‰ f · C 'D @AB 9 3 ‰f q ce Ï r s e ‚c b if Ì ™Ë r r h rc Ü ÜÝÖ Ð p e c v d wq c e d r i} ‰e Ú ÛÍÓ h r i Ì ™Ë Í ™Ë Ì w h p Ï Ù e t c rt p p f s t } ‰ i‘ r w c h cf x‰ c u Ì ™Ë d 8 8 r dt e r 8  } 7 rq i} ÔÐ Ì ™Ë h ÑÒ % 3 6 20 ‰ 5'4 eh ÙÌ pw & te 10 s f i rf i dp c h dc c ) 320 1 ‰ ) '( t g br ‚c 3 wt c he d i Ñ Ð ÏÞ ÑÒ c c f  f g i Ó Í Ô ÕÓ p ec c Ö w ‰f p e is d p f £ e u h i b Ð Ð iŠ} r Ú ÛÓ ie ‰ if r i Ö e p c hg t ‰ e r Ü t ds r e bÐ f r ÎÏ c v b fc ÙÌ h c i r h f × ØÐ Ó vh rt xh b f e p f c d d h f rt de c } }f c v} i t } c z i ‰e c x v wh c s e s ab r f f r cf ‰w dv t dc u f r i  } ce i w d pw p e i} Œ t ab h i d i e ‰ he t fh ‰w v i‰ t f c vp rc d r c c d i e de pf e }i c s xh b e • t u r UT e H v bt EF Q } —É r d de S e — c f U r G c G— P S c p rt —É i q dc }f ec w xs d p s e t r d wp t g ds h c Ê e wh p $& &'% $ Ï Ú ÓÍ Ð C C 'D @AB 9 fh i Ì ™Ë e 㠜РÙx p rt Ö i p f br r u c e r r c Ó Í 3 c ß b ÚÓ r r tf ß ÚÓ p b Ó i ÙÌ w  â àá d de d }i e ×Ð Ó eh Ì ™Ë i b cf Ð Ö 8 r ÎÏ ÔÐ Ö Ôß 8 8 7 ‰ Í ÎÏ Ñ % 33 f ÑÒ ÏÞ ÑÒ c Ö ÑÒ ÌË Í Ô ÕÓ 6 20 e b Ù ÌÍ Ñ ÏÞ ÑÒ 5'4 fh & r cf â àá 10 ip c ) 320 1 dc Ãc ) '( t br p $& &'% $ h c }  h de w z eh e } d f r cf ce i ie if b ƒ ~ j~ í ƒ   # §  eh  rc h br î ¨§ © if r b f ï æ { © e æ ä ª §Ÿ ƒ dc c ¦ ö ü ç ó éh è¦ ¢ ú e ~ rc í ò ò e ¡ø f if d o¦ ð ñ~ dt £þ ôø õ j ð ñ~ dc jª bt ‰ ð ñ~ • f } } ‚ i d © { f ú r ö c u æ ÿ þ g å í þ ~ d ƒ he j ~¦ i l r p ûü e ~ j j§ h  ó  ý   õ x © æ ¥  © { æ  ûö æ æ©   §  ûú æ© ¦ ƒ  øù © â àá j§ ÷ö dt u   õ j§ dt í Í ™Ë Ì z ÷ i ab r ôü eˆ ß Ö { Ó é‰ è ‰ dt fq r i r i æ ÙÌ r ƒ p eÐ ÎÏ p j ~¦ cf f t !" c z i e bc éc r dc c t u ©è æ© hf v} c dt j b f u r h f } w ÌÍ Ë e z  e } æ © v de r  ce c lì b f l uÐ ëê h jä dt b Ž ˆ c }v f l r i c b æ r cf æ b æ æ© c D Ÿè r i ‰ e r tf p çxˆ Ð t t u f ÎÏ e c b dt p cf z e d eh i b f t u ©å æ r cf æ æ © e r tf c v} ŸåD c c u u © §¨ ôó ¤¦ u ¦§ ¥ ¤ 5 ‘ ‘ ‘ ‘ ‘ ˆ  # § !"   w † † ‘ ‰ w † † † ‘ † w † ‘ † ‘ a q ‘ ‘ ‰  y t y † † ‘ V RP ‘  w ‘ ‘ c C v  y u U H  q p x ˆ he ig dw a XF QW ˆ C 9 78 5 64 G c 3 † ‘ † ‘ y † ‘ † ‘ ‘ ‘ Ds r B  U ' % 2  a b` D Y G 0 1) a ef Q ‡ í ‰ ‰ ‰  q GF (' p & H AT pì ‡  $% ‡      ‰ SF    ë Q RP … B ‡ I ˆ ˆ ‡ í ‡  ˆ h i fg e D H ˆ ¥ ˆ   ‰    p d x C §  a„ ‡ A † † ‡† † † ‡† † ‡ ¦  H aY ƒF he ig G EF © ‚ dy DC F B   U SG F X A@ © §¨ a b` € ¤¦ T ¦§ ¥ ¤ C ƒ ˆ DF  Q   # § !"   ‰ y ‰  ‡  ” y  y  ‰  ‡ ‡ ˆ ” ˆ ” y ˆ D y ˆ  B y ˆ ‰  Q EF ‡ D P ˆ B ‡ ” • ‡ ” w ” ‰ w  w w D  H  H AT a a a ˆ  ‰ y ˆ  y  ˆ  a  A s SF y ‰  y ¥   ‰     QC ‡ ‡ §  ‡ ‡ BF ¦  © “ EF C   D S © §¨ ’ ¤¦ ¦§ ¥ ¤ C F  ‰ # § !" B  D  SF GF QP D˜ SG F E B DI Q W H A SF SF C A ’ G EQ B £ A U sC IF q E C A U— SA C AT Q F f C DF H G D y E U Q Q f e Q XU B G D ‡ EF B AT n EQ SF ”t B Q e ” D F V– F C F Q E w e e e a m w n DF X U k e ‡ A GE G CA sG B H Q ƒ hj U U B „ k ‡ˆ     e ¥ a EA m y   F l   §  AE t a th £C Q g ¦ E ˆ  B a B © EA y e s C w AE E ˆ ˆ BF G w Q „i S U v a D U CV C Q F A A Q S QT F QC G U™Q F XF SF QW SG F ’ F   f H XV C © §¨ ed A ¤¦ ™ Q ¦§ ¥ ¤ ƒ hj n f „   # § !"  f e w m e w    ¥ EA y  p E p B f a m  f y e ‡ ” „ n f a k s tv ‡f w AE t a ” „i   k F n   ‡p th g §  w AE v a e ¦ E „  B © ap EA y F   pqr © §¨ eo ¤¦ ¦§ ¥ ¤ y Ž  #  … | } ~ !"  xy{ { w} „ y  € x § | €  ‚ ˆ zx  zx ‚ ~ ‚{ | xy y w |y ~ | …‡  | ƒ {  y  y |  | x y  } ƒ w  ~ y | Š‡ y y ƒ … …  ‚w y ‚w € ‚w €  | |y {  xy € …‡ y w} | |~ ~Œ | y ‚{ y w ~… y w} y zx ‹ zx † | y   {x    | ~  y ~{ zx  wy ‰w x {x ¥ w     | ‚ Š w ‚ … §  ‚ € ~ zx y ¦ ~ } € wxy   y ©  w w y v … …   u u © §¨ ¤¦ ¦§ ¥ ¤ H B  ¡ # ™ P C U – Ÿ G “™ GC CA A F CA G ™ E A £C F A — B nX AT   ”t  –  œ — • f e Q §  Q A C F A HA t t AT G G “™ A H — —q ™ A GC SF ‚ £ ž F – U™ ‚ G G‚ ž U Q S D G Y IF “™ D H B A U — GU ¥ m s  t §  Ÿ › Rm £e W ¦  c © GC CA GU E v a G A B q XF CV   – › › CQ F  — a A Y C X SF n ™ D Q !" C  DU CA B A Q QC DC A q D A ™ B — C AT F – • A S C E Q ™ šD A ’ G DA S D CA B s U ˜r C ™ H r l k Q — n D •s 4 CA H Q %’ B GC Q CA D 98 F ™ BF ƒF P U 78‘ Q UQ G 0 & Q C 7 % & AT 5 EQ G  D “™ H A — P B DC U F V B C F Q A‚ H ‚ XV F   U ™ f e X— V” A@ ` ‚ © §¨ e A Y ¤¦ G X ¦§ ¥ ¤ B ¥  — AT G “™ H A f — W C ` f e Y E™ X f a H ” # B E B SF “™ A s U ` A A e ” c BF A Y – “ q CA e a D Q c  D   ™ C D A B BF  Ds s¤ ¥ V T CA “ X  AE a ¤    E D B q §  EA X A Ds ™ n !" CA  ‚ SF QC F ™ D A Qf CQ P F ™ V E A ™B D U sq f c AT U UQ G G Q f W G FI B Q n F U H s D B D D CA CA B § GC  F ™ A G S U™ SF F B T EF D ` A ™ B Q D D B H H AT A ƒF P s SF B ƒ CQ D CA F f — Q V ™ G— AT £ F  FI X S F B A H XV SF A ™ Q SF GC QP G F¢ F ™ ¦ F  D A B © £ ‚ G X S AE ¤ a H G   E XV A s U™ B GF ‚ € © §¨ EA A@ F ¤¦ ¦§ ¥ ¤ C C F S W F B™ ’ B “ s C  ª # § A SF Q D Q A U™Q X GF G A C Q EF Q F CA U F ™ C ™ — D C ‚ A F G CQ X ™ GF G U SF EF A ‚ S U Q U™ S C X  V U Q q  F H U A G C S I ¥   SQ G IF    §  EF ™ E™ B VC U F ¦ D  A U CA A C UQ E™ GF ‚ £ ™ H DC GC F — G— SF ™   H C S A Q V ¤¦ F A “ © §¨ B U™ Q Q © U A S AT G— — F F SF F ¦A s G   F C £ SF s !" E   A DA G Q G‚ BF SF “ D U F Q G SF D Q UQ SF B AT QC F F — B X G A A E ‚ H HA U Q V G GF B B C GC B B™ D B F EF B U F‚ P U U B A BF A s GC CA G GF ‚ F sT ™ T SF A C Q G Q D§H s H ™ C DC E A BF DC H H £ EF ©Q F ™B Q ¨ U Q s Q S ‚ S G B “U Q C B™ U SF F DsH A s U P B D ‚ ™ UQ ’ ‚ F D A sq UQ G s Q S DC U H G Q U U G S V ™ Q D F AE G‚ ¦A C A P Q D A SG F “ G G U U F — D H V U I D £ Q  EF B A B A D D E A B U DH ¤ H P H H D B U U H S U sP F P B C S SQ ‚ V A W B U S Q EF C B A ™ D C F SF ‚ G “ A C A D H X C U P P V A DC A U G QP B DH D ™W Q ™ SG F H F U Q C QW U DC X C G C F HA AT X TU V EF H Q A ™ H Q A BF A ™ C Q FP Q C D S ’ A Q A X ¦§ ¥ ¤  # # § !" C D  Y  s A B H E ™ £e XV A c B U “™ H e A ` — S S Q D ™ šD Q SF P T B Q H U ƒF P UA Q S U — t – Q G CA F Ÿ Q B X VC C GC U  CA  H XV   F F ™ A ™ A B T “™ H ¥ ‚   G   B D CA A §  D S — ¦ G IF S D Q  Q C D © D S E T   Q T F «G A AT £ © §¨ G CA ¤¦ Q ¦§ ¥ ¤  ‰ # § !"  B  SF QC F ™ B D E B SF D B QC F ™ D H E XV ƒ EF B A D ™ A ™ B — P B “™ h H D A H XV — H W H AT Y s “™ — H — – e a A t – — ` e e W Ÿ i Y m – i  FI X a ¤ H „ s t Ds  A   C A BF „ ¥     CA §  D B AE a c A ™ f e ƒF P A s n D ™ D i q n q D E T “ ¬ ­c AE ¤ a B CA D AC e ” f ` A s X U SF A BF G QC ” Q H CA X A@ G A s S GF ‚ D Q r GC F ™ ‚ a ¦ h Ds F i n A  © G F¢ G £ S AE a   E D U™ © §¨ B AT £ € AE ¤¦ F ¦§ ¥ ¤ © ˆ ‰ # § !" Q FP   ¨ A QC B A D QC F H V BF GC U I CA EA £ F  ™ F A EF — “ B ‚ G G D H Q H A ¤ BA U sT H H E A U H C Q DH S V X H P A U A sG r V C T D ™ H A S S s A G ’ A B U – QP D P B B£ DC DH B ™B U ™W DA sH V B U U ™ Q U H D B F Q D BQ   S ‚   C F Q D B F DC ‚ U ¥ SG F X   C G C EF A F W §  ¦ G V D  C “ U HA U © G C A H C ‚ DC   UT D S © §¨ ™ ’ H BF X   U Q C — D H F W SG F GC DsH Q F F ™ Q ¦A ¤¦ A ¦§ ¥ ¤ S G G P A sC U™ F F U BG F  ‰ # §  IF F A A — F Q X A GC CA A F Q — S AT F X VC ³— ™ t H i Q B CA F F ™ A‚ X Q G – Ÿ S U™ GC C A ™Q EF A A A A ‚ G sG C E H H™ DC s H U G C A F D G Q FI AT BF A  Q  i D S Q  “  SF DA G ¥ U   QT BG V G A QC A E B   BF D E SF F §  ¦ U s H  SQ © P SF U F V U EQ XV B A ™ A   V ™ E ™ H ‚ A U © §¨ S U™ U ‚ IF  C E B DI F C BQ D h ‚ G B QC G D s U S D Q ‚ G D CA UQ GF G‚ Q BF G U™ F X H AT A B ™Q B s S B G‚ P Q CA A U s D c X ™ H ´F ™ ‚ G P B D EF SF B G SF B V E C F U B DI U – i H D Q HQ B B “™ H U H— ‚ ³t q BQ Q CA DF G‚ A QC Q G G C s D i C B U E F D D U Q U A GC H V U HQ D XV — U™ – A CA SF U ™ HQ U™ s SF EV B XV s ‚ GC CA G ² Q F G A ™Q BQ A ‚ °± ­¯ H FI F “™ H — B X P F E U A X CV U U™ SF D S B E U ’ F B Q F V P U A ™ — t C F Q Ci m A – i !" h H Q VC BF F D Q D A QP ™G AE A V C F F U D B B SF GC UQ q Q XV F SQ ™ SF S A X D S GP HA B U Q DU C s — U At HQ ™Q H ™ C HF FP ™ Sr U ™ C Q P B F F ™ Ÿ D G EV ™Q q ± F GF ® D G G µ¦ V Q ¦§ ¥ µ SF S B SF GC H S XV F X A H S BF FI X B — A QW U ‰ ‰ # § !" CA F GC ™ C A ‚ G ™ H G U BF D G Q A s B C D A DA ³· U IF Q Q C F ³ “U F Q V‚ A FI U— ‚ s A IQ X U— H A S U ™ X  X ¨ A ™ F D C Q S AT X HA D G “™ GP H HA s A U SF HA H  —  U Q C H EF V ¸ ™ G A §  G‚ SQ ¦ U D  © BQ Q   UQ G D s Q   G s AT A  BF  X G C  D SF X F A s “U s SF Q X   GC Q V DC Q B E F U IF DP V A “U A Q DA DC C P C B U U F A‚ U HF H V U H C F SF B U C DC S ’ B A © sG C E U V G CA F GP SF U Q Q ‚ ‚ F U Q SF F‚ Q V B G IF ³¶ A C Q U— A F C A   s GV D Q A SF DU Q ™ — Q G T D ” A G “U © §¨ ™ F µ¦ A A s Q IF H A G A C F C SF X ’ A‚ G A Q X BA X D IQ GF ‚ W Q A ™ A D s Q s B BF P B ” T B C HA “™ A D GP ‚ G U AE BQ D A Q ™ ™ IF U— X s B G S S IF X D DP Q SF F U ³ P SF H H HQ Q EA D Q HA A S “™ A GC s IF B™ — A E G U U S ™ A F V IQ ™ D B C X G A s G‚ F SF — C F G F GF ‚ IF Q V IF ³ X U H CA X sG GF ‚ U ‚ X ¨ C HA DA B Q B E D X A GF sG C D  U U U BA C D H XV F ™ F X A ™ E A sG C SF ³ — C DA E H G q H ‚ F U “U D “ EF GF ‚ SF F  W UQ ¨ H SF Q GF ‚ U X D Q  C Q C B GC T D s DC W C ™ A A E ™ D ³ Q CA IF B A DP C G A U A W H S — B X D Q A E A GP HA U GP HA Q X Q G A s AT GF ‚ GE B U U B ’ C G B H XV BQ BF U Q A ™ H A SQ U ™Q Q A SQ — G ™ D S G A «A D s U Q S S — Q F F G EF Q ¦A G G A Q T ¦§ ¸ µ SF B F B Q Q W BA D SF X B Q  ‰ # !"   SQ A F H V Q U I “™ H T ™Q A SF — EV ‚ F BQ A — AT F B ³ U ‚ G S S U ‚ U IF Q ™ Q G A DP A ™Q P GF P GC U IF CA B D§ C Q F‚ HX “™ EF H P H — H U U s U A   G‚ W   V F HD Q F SF D A U ¸  DC Q C   BF U Ç  A‚ F A Æ “ EF  © B F SG F U D A H G Q S VC Q © ÇÈ C F F A Q G   EQ Q Q FP U Q V EF G F EF F GU ‚ U B F A B A IQ E HF DC Q ¨ ™ C  A ‚ ‚ B™ D A A D Q Å SF s  ¨ H XV A ™ CA A F G ™ A BA ³C G B V H SX F ™C D F GC s CA C A Q G DA Q DH F GB P B F DC s GV ™ S U G EÄ F B GC U H G F ™ U F X H™ U °Â G F C EV G “U DI A E U U V  D A ‚ G  — “ E P X F B™ W U QW P F A G ½¿ ¾¼ G G A s ‚ F ™ U BF P Q G EF BF B C F‚ HF FI SF DP A ™ Q ‚ F U ™ s S U °Â “U U V U S S Q A º» D X GC E¹ BQ P Q ³· U V X A D E C F U Q U ™ XC Q D B EF © U ™ P E B B Q A SF F EV H  F SF Q E C™ Q A A HQ À°Ã GF H sG C U Q Á Àà BQ Q ± D F U F U CA G F‚ F °ÃÀ ‚ QC C F Á ­À FI Q ‚ H U™ s F A DH Q U— FP CA SF I U C G D S ¢ B G Q U D Q S CA C  F A G D S ‚ G D H G HA G‚ A Ç C I D S Q D A BQ HA T F DA D AT U SA GE Q V F B — D U GB U ™ A ™ C XV D B SF s H C F Q E s B B U DU U B C Q U C “U D U G IQ ³ Q H  ¨ A‚ GC ™ Q D U s A BF s CQ F U Q A F Q V‚ A ‚ GP U U X ™ µÆ V G ÆÇ ¸ µ E B DH Ž ‰ # Ç !"  ™ A Q SF CA EQ C X EF QW H C W U U — B S XF D CA U B U ‚ C QW ™ ™ C S C Q P F © Q D H HG F H ‚ Q V V X BF “U X G Ds H “ EF V DA B S ‚ D F ™ D H Q UQT G BA C F‚ GV ³C E V E B B F s A B C “ U D Qq D Q U E X ³ S ‚ A U P B F EF H Q U U Q SF s U C A EQ B V C F F Q  F  A — XF B  V E H ‚  F — ¸ V   A D   A Q S F Ç  F T D B™ D§ ™ Æ GF D  U © C T   G A GU EF © ÇÈ ™Q F C G™ G W F T U Q W ’ F U F‚ B™ SF X F Q P F Q DP QC Q Q D s B A B G D H SF A‚ D CA C P B A B EF Q F‚ U Q B s XP CA U Q F D S D G EF X — DC C C F SF B Q F U Q E A U B AT sG C S F B™ D F P D HQ ’ F F‚ A D IA B™ EF QT ³ F B™ s P CA B AE U B F‚ W GF HD Q EF P C F ³ ™ DH SF Fq W CA G QW  F U Q E DA E E B BQ U F C B P B A H B S F D C A Q D S G ‚ V G U s A Q G FI SF D ™  C “U C U F B U D D Q B X XC s A C Q D G‚ A ‚ EF CV S G B “ G Q BA ³C EF C BF F AE W D P U G H q A Q ³ A‚ A Q H C F Q Q F B SA DF D C T DH BF X ´F D S W UQ U™ Q E™ U X «G A V G— IF µÆ G G ÆÇ ¸ µ 51 41 31 21 62 52 42 32 22 63 53 43 33 64 54 44 65 55 11 61 66 µ ÆÇ ¸ µÆ ÇÈ ©    © Æ Ç      ¸       !" 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This note was uploaded on 07/21/2011 for the course CIS 5930 taught by Professor Staff during the Spring '08 term at FSU.

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