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Sign Sign Presentation Transcript

  •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f&2-$J&,-$O>0+8,2/9$H1.*,)9*/&1N .3&=$*32*$&),$2>0&,/*3'$+44+9*/?+>@$+>/'/12*+.$*3+$'2Q&,/*@$&4$./01$ +D*+1./&1.A$ I3+@$ 2>.&$ .3&=$ *32*$ /*$ ./01/4/921*>@$ /'(,&?+.$ GH/NJ7<-5-(/.-*0/)J()0.-+0/I88&KLM/)J(.O/B!KLM/.J(H (+,4&,'219+<$ =3/>+$ /*$ /19,+2.+.$ BHI$ 9&'(/>2*/&1$ */'+$ 8@$ &1>@$ /$g$'+'h $$$$$$$7$M!N RA!!SA$J+$/'(>+'+1*+-$&),$2>0&,/*3'$4&,$(,&0,2'.$/1$B2?2<$8)*$ /$g$/$i$!h $$$$$$$7$M6N /$g$+D*+1-M/Nh$$$$$$$7$M5N$$bb$+D(>/9/*$./01$+D*+1./&1$/.$,+E)/,+- /*$921$8+$2((>/+-$*&$21@$>210)20+$,+E)/,/10$./01$+D*+1./&1.A$ *$g$M-&)8>+N$/h$$$$$$7$M;N$$bb$$$').*$8+$./017+D+*+1-+- M+D*+1-M$N$-+1&*+.$2$./01$+D*+1./&1$/1.*,)9*/&1$4,&'$5678/*$*&$:;78/*N &'()*+,-)./'01/#234)5(/6).5,-7(+,./
  • +%,-).%'("/)#01' ' 2"0$%"'3).)#)4%' 2".7"'8-0-)&9$':);"&)#"&7' sign extension /)B'D)/)#"B'()4)E)*)B'>A>@FGH>B'I)J)4'' /)#01B'4).)#)4%'NOLJP%;/P9"/'' ' R RR$$$$$$$$$$RR R $*&$:;78/*$ :5 56 5! R :5 56 5! R @$2,+$.*/>>$ $ .(+9/4/+.$ ! !!$$$$$$$$$$!! ! )93$ B2?2$ :5 56 5! R :5 56 5! R $ 1@$ 5678/*$ F-*2,)/@A/#-*0/)J()0.-+0/+P/'/QGR3-(/S'<2)/(+/'/KLR3-(/S'<2)/ ,$ /1*+0+,$ -A$ H1$ *3/.$ @H/B97<-5-(/I'2(+9'(-5H/.-*0/)J()0.-+0/I88&KLM/<?'H /'/12*/10$ . .$.$$$$$$$$$$.$. . HKL$B2?2$ 5! R :5 56 5! R *2>$,+.)>*.$ >=2 Mf&2-$J&,-$O>0+8,2/9$H1.*,)9*/&1N *@$&4$./01$ /'(,&?+.$ GH/NJ7<-5-(/.-*0/)J()0.-+0/I88&KLM/)J(.O/B!KLM/.J(H $ 8@$ &1>@$ /$g$'+'h $$$$$$$7$M!N B2?2<$8)*$ /$g$/$i$!h $$$$$$$7$M6N /$g$+D*+1-M/Nh$$$$$$$7$M5N$$bb$+D(>/9/*$./01$+D*+1./&1$/.$,+E)/,+- 1.A$ *$g$M-&)8>+N$/h$$$$$$7$M;N$$bb$$$').*$8+$./017+D+*+1-+- M+D*+1-M$N$-+1&*+.$2$./01$+D*+1./&1$/1.*,)9*/&1$4,&'$5678/*$*&$:;78/*N F-*2,)/GA/$?+/(>7)./+P/.-*0/)J()0.-+0/ '()*+"$,%-
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  • ':'(@$ /1)*(;8*/+1$ !$ *&.*$ ('J;/(')$ .$ )/01$ '>*'1)/+1F$ ;14'))$ *&'$ /1*$*$_$Xa$WW$"$/)$.$<9C=/*$:.(/.=4'$ $ /1*$*$_$Xa$WW$"$/)$.$<9C=/*$:.(/.=4'$ '>'8;*'3$('0/+16$N/1.44@F$/1$*&'$*&/(3$-&.)'$GG<HC<HF$('3;13.1*$)/01$ )+;(8'$ +-'(.13$ +,$ *&'$ /1)*(;8*/+1$ !$ /)$ 0;.(.1*''3$ *+$ ='$ )/01C /1*$/$_$?'?a$WW$#$/)$.$<9C=/*$:.(/.=4'$ $ /1*$/$_$?'?a$WW$#$/)$.$<9C=/*$:.(/.=4'$ '>*'13'36$ K'$.('$ '4/?/1.*'3$ ;)/10$ UVWVU$ 8&./1)6$ %&'$ ,+44+5/10$ '>*'1)/+1)$ ;)'$ *&'$ ,/()*$ .--(+.8&$ /1$ +(3'($ *+$ ?+)*$ ',,'8*/:'4@$ /$_$'>*'13G/Ha$ C$G!H$ /$_$'>*'13G/Ha$ C$G!H$ (3)-1 Sign Extension Insertion $G<H *&(''$)'8*/+1)$3')8(/='$'.8&$-&.)'6$ 3+$b$ $ 3+$b$ +-*/?/2'$ )/01$ '>*'1)/+1)6$+,-./0# 2$ /)$ .1$ '>.?-4'$ *+$ )&+5$ *&')'$ $ /$_$/$C$!a$ C$G9H$ /$_$/$C$!a$$ C$G9H$ *5+$.--(+.8&')6$L1$*&/)$'>.?-4'F$/,$*&'$8+?-/4'($0'1'(.*')$.$)/01$ /$_$'>*'13G/Ha$ C$G<H$ $ /$_$'>*'13G/Ha$ C$G<H$ $ !"3# 4,-5#678059,:5#;590/8,:5# '>*'1)/+1$.*$.$;)'$-+/1*$.)$/1$G8HF$1+$)/01$'>*'1)/+1$8.1$='$'4/?/C M$_$.Q/Ra$ C$GAH$ M$_$.Q/Ra$ C$GAH$ $ 1.*'36$L1$8+1*(.)*F$/,$*&'$8+?-/4'($0'1'(.*')$.$)/01$'>*'1)/+1$.*$.$ L1$ *&'$ ,/()*$ -&.)'F$ 5'$ /1)'(*$ *5+$ D/13)$ +,$ )/01$ '>*'1)/+1)6$ %+$ M$_$'>*'13GMHa$$ C$GBH$ $ #$%$&'(")*+"*,-*-.#/$0$.12/$ 3',/1/*/+1$ -+/1*$ .)$ /1$ G=HF$ +1'$ )/01$ '>*'1)/+1$4++-)F$ 5'$ /1)'(*$ )/01$ M$_$M$c$X>X,,,,,,,a$ C$GEH$ M$_$'>*'13GMHa$$ C$GBH$ 1$ '>*'1C '4/?/1.*'$ )/01$ '>*'1)/+1)$ ',,'8*/:'4@$ ,(+?$ 8.1$ ='$ '4/?/1.*'36$ M$_$'>*'13GMHa$$ C$GTH$ $ M$_$M$c$X>X,,,,,,,a$ C$GEH$ (.1)4.*')$ G7''$7'8*/+1$<$,+($*&'$*&'+('?)$*&.*$M;)*/,@$*&/)$'4/?/1.*/+16H$ /)$ *&'$ '>*'1)/+1$ /1)*(;8*/+1)6$ L1$ *&'$ '>.?-4'$ +,$ +,-./0# <F$ G!XH$ *$`_$Ma$ $ C$G"H$ $ M$_$'>*'13GMHa$$ C$GTH$ $.$<9C=/*$ +14@$/1)*(;8*/+1$*&.*$('J;/(')$.$)/01$'>*'1)/+1$,+($"6$L,$)/01$'>*'1C *$_$'>*'13G*Ha$$ C$G#H$ $ *$`_$Ma$ $ C$G"H$ 7*'-$ G9H$ .4)+$ +-*/?/2')$ )/01$ '>*'1)/+1)6$ N+($ '>.?-4'F$ 5&'1$ .$ d$5&/4'G/$e$)*.(*Ha$ *$_$'>*'13G*Ha$$ C$G#H$ .('$ *5+$ )/+1$'4/?/1.*/+1$/)$.--4/'3$&'('$5/*&+;*$/1)'(*/+1F$*&'$)/01$'>*'1C $ 8+1)*.1*$/)$-(+-.0.*'3$.)$*&'$)+;(8'$+-'(.13$+,$.$)/01$'>*'1)/+1F$ WW$1''3$.$)/01$'>*'1)/+1$,+($"$ d$5&/4'G/$e$)*.(*Ha$ $*+$0'1C )/+1$G#H$5/44$)*/44$('?./1$/1$*&'$4++-$.)$)&+51$/1$+,-./0#=G.H6$%+$ 3$_$G3+;=4'H*a$ C$G!XH$ $ WW$1''3$.$)/01$'>*'1)/+1$,+($"$ .*$/)$/?C .:+/3$*&/)$/1',,/8/'18@F$5'$/1)'(*$.$)/01$'>*'1)/+1$/1)*(;8*/+1$/?C HAJ#$/,-,5A>#E/:-/AB $ "$%$*+"*,-."/3$ 0$.11/$ )*/1.*/+1$ ?'3/.*'4@$=',+('$':'(@$/1)*(;8*/+1$5&'('$)/01$'>*'1)/+1$/)$1'8')C $$$*$_$/$`$Ma 3$_$G3+;=4'H*a$ C$G!XH$ $$$.Q*$`$!R$_$Xa ).(@$ ;14'))$ /*)$ :.(/.=4'$ /)$ +=:/+;)4@$ )/01C'>*'13'36$ %+$ =.4.18'$ /+1$ !$ /)$ $$$3$_$G3+;=4'H$*a +,-./0#<"#67ABE>0#:C#,590/8,5-#A#9,-5#078059,:5# '$ .$ )/01$ $ HIJ#'C80/#,590/8,:5# $ HIJ#K050/A80#A#9,-5#078059,:5#AC80/#@0C,5,8,:5 HAJ#O0C:/0#,590/8,:5# # HAJ#$E8,B,G0@#/09.>8#?,8D:.8# HIJ#$E8,B,G0@#/09.>8#?,8D# @$ =',+('$ $$$G=',+('$'4/?/1.*/+1H $ /1*$Ma$WW$!$/)$.$<9C=/*$:.(/.=4'$ G.,*'($'4/?/1.*/+1H $ /1*$Ma$WW$!$/)$.$<9C=/*$:.(/.=4'$ ,590/8,:5# ,590/8,:5# 4'))$ *&'$ $$$*$_$/$`$Ma /1*$*$_$Xa$WW$"$/)$.$<9C=/*$:.(/.=4'$ *$_$/$`$Ma $ /1*$*$_$Xa$WW$"$/)$.$<9C=/*$:.(/.=4'$ $ $$#8#L#07805@H#8#JM 8#L#07805@H#8#JM /1*$Ma$WW$!$/)$.$<9C=/*$:.(/.=4'$ /1*$Ma$WW$!$/)$.$<9C=/*$:.(/.=4'$ ='$ )/01C /1*$/$_$?'?a$WW$#$/)$.$<9C=/*$:.(/.=4'$ $$$*!$_$*$`$!a $ /1*$/$_$?'?a$WW$#$/)$.$<9C=/*$:.(/.=4'$ *!$_$*$`$!a /1*$*$_$Xa$WW$"$/)$.$<9C=/*$:.(/.=4'$ $ /1*$*$_$Xa$WW$"$/)$.$<9C=/*$:.(/.=4'$ ,'8*/:'4@$ /$_$'>*'13G/Ha$ C$G!H$ /$_$'>*'13G/Ha$ C$G!H$ /1*$/$_$?'?a$WW$#$/)$.$<9C=/*$:.(/.=4'$ /1*$/$_$?'?a$WW$#$/)$.$<9C=/*$:.(/.=4'$ $$#83#L#07805@H#83#JM 3+$b$ $$$.Q$*!$R$_$Xa $ 3+$b$ $ 5$ *&')'$ $ .Q$*!$R$_$Xa 3+$b$ $ 3+$b$ /$_$/$C$!a$ $$$3$_$G3+;=4'H$*aC$G9H$ /$_$/$C$!a$$ 3$_$G3+;=4'H$*a C$G9H$ /$_$/$C$!a$ C$G9H$ /$_$/$C$!a$$ C$G9H$ ')$.$)/01$ /$_$'>*'13G/Ha$ C$G<H$ $ /$_$'>*'13G/Ha$ C$G<H$ $ M$_$.Q/Ra$ C$GAH$ M$_$.Q/Ra$ C$GAH$ ='$'4/?/C HNJ#K050/A80#A#9,-5#078059,:5#I0C:/0#.90 M$_$.Q/Ra$ C$GAH$ $ # M$_$.Q/Ra$ C$GAH$ $ $$$G=',+('$'4/?/1.*/+1H G.,*'($'4/?/1.*/+1H M$_$M$c$X>X,,,,,,,a$ C$GEH$ M$_$M$c$X>X,,,,,,,a$ C$GEH$ )/+1$.*$.$ M$_$'>*'13GMHa$$ C$GBH$ $ #$%$&'(")*+"*,-*-.#/$0$.12/$ *$`_$Ma$ $ C$G"H$ $ *$`_$Ma$ $ C$G"H$ $$$*$_$/$`$Ma M$_$M$c$X>X,,,,,,,a$ C$GEH$ *$_$/$`$Ma M$_$'>*'13GMHa$$ C$GBH$ ?/1.*'36$ $$$*!$_$*$`$!a $ *!$_$*$`$!a *$_$'>*'13G*Ha$$ C$G#H$ $ $ M$_$'>*'13GMHa$$ C$GTH$ $$$83#L#07805@H#83#JM M$_$M$c$X>X,,,,,,,a$ C$GEH$ 83#L#07805@H#83#JM d$5&/4'G/$e$)*.(*Ha$ d$5&/4'G/$e$)*.(*Ha$ 16H$ *$`_$Ma$ $ $ $ $$$.Q$*!$R$_$Xa C$G"H$ M$_$'>*'13GMHa$$ .Q$*!$R$_$Xa C$GTH$ WW$1''3$.$)/01$'>*'1)/+1$,+($"$ WW$1''3$.$)/01$'>*'1)/+1$,+($"$ *$_$'>*'13G*Ha$$ C$G#H$ $$$8#L#07805@H#8#JM $ *$`_$Ma$ $ 8#L#07805@H#8#JM C$G"H$ 3$_$G3+;=4'H*a$ C$G!XH$ $ "$%$*+"*,-."/3$ 0$.11/$ 5&'1$ .$ d$5&/4'G/$e$)*.(*Ha$ *$_$'>*'13G*Ha$$ C$G#H$ $$$3$_$G3+;=4'H$*a $ 3$_$G3+;=4'H$*a $ 3$_$G3+;=4'H*a C$G!XH$ >*'1)/+1F$ WW$1''3$.$)/01$'>*'1)/+1$,+($"$ d$5&/4'G/$e$)*.(*Ha$ 3$_$G3+;=4'H*a$ C$G!XH$ $ WW$1''3$.$)/01$'>*'1)/+1$,+($"$ +,-./0#2"#F?:#AEE/:AND09#8:#-050/A80#9,-5#078059,:59# +,-./0#="#FD0#:E8,B,G0@#/09.>8#:C#+,-./0#<# $ "$%$*+"*,-."/3$ 0$.11/$ 3$_$G3+;=4'H*a$ C$G!XH$ +,-./0#<"#67ABE>0#:C#,590/8,5-#A#9,-5#078059,:5# !"#$ $ HAJ#$E8,B,G0@#/09.>8#?,8D:.8# HIJ#$E8,B,G0@#/09.>8#?,8D# ,590/8,:5# $ ,590/8,:5# /1*$Ma$WW$!$/)$.$<9C=/*$:.(/.=4'$ $ /1*$Ma$WW$!$/)$.$<9C=/*$:.(/.=4'$ /1*$*$_$Xa$WW$"$/)$.$<9C=/*$:.(/.=4'$ $ /1*$*$_$Xa$WW$"$/)$.$<9C=/*$:.(/.=4'$ /1*$/$_$?'?a$WW$#$/)$.$<9C=/*$:.(/.=4'$ $ /1*$/$_$?'?a$WW$#$/)$.$<9C=/*$:.(/.=4'$ 3+$b$ $ 3+$b$ /$_$/$C$!a$ C$G9H$ /$_$/$C$!a$$ C$G9H$ M$_$.Q/Ra$ C$GAH$ $ M$_$.Q/Ra$ C$GAH$ M$_$M$c$X>X,,,,,,,a$ C$GEH$ $ M$_$M$c$X>X,,,,,,,a$ C$GEH$ *$`_$Ma$ $ C$G"H$ $ *$`_$Ma$ $ C$G"H$ *$_$'>*'13G*Ha$$ C$G#H$ $
  • 2,+,)2,)%+*$/+,+$&-$%&-/),)&-+*$G7+-%6.29$:6.-$,6.$)-,.7(7.,.7$0)-/2$ (3)-2 Order determination ,6+,$ +$ '.,6&/$ )2$ .F.%8,./$ 07.V8.-,*53$ ,6.$ /5-+')%$ %&'()*.7$ )2$ %+**./9$T,$,6+,$,)'.3$,6.$)-,.7(7.,.7$(7&1)/.2$,6.$2,+,)2,)%+*$/+,+$,&$ ,6.$/5-+')%$%&'()*.79$ A-B$C(/.&($(1!+!,-*!., AFB$G(941*$@ AHB$G(941*$" $$)$P$O$g$I_ $$)$P$O$g$I_ $$)$P$O$g$I_ $$!$D$(8*(,'A!BE $$!$D$(8*(,'A!BE $$/&$^ $$/&$^ $$/&$^ $$$$$)$P$)$g$!_ $$$$$)$P$)$g$!_ $$$$$)$P$)$g$!_ $$$$$!$D$(8*(,'A!BE $$$$$!$D$(8*(,'A!BE $$$$$+A)C$P$#_ $$$$$+A)C$P$#_ $$$$$+A)C$P$#_ $$b$46)*.<)$h$.-/@_ $$b$46)*.<)$h$.-/@_ $$b$46)*.<)$h$.-/@_ $ 2!34&($5#$08-+I1($&(J4!&!,3$.&'(&$'(*(&+!,-*!.,$ "#6$ 7!3,$08*(,9!.,$01!+!,-*!.,$ D6.$;&+*$&0$,6)2$&(,)')X+,)&-$)2$,&$+-+*5X.$+-/$.*)')-+,.$.+%6$2);-$ we eliminate sign extensions starting from the most .F,.-2)&-$ 2,+7,)-;$ 07&'$ regions. 07.V8.-,*5$ .F.%8,./$ 7.;)&-3$ /.E frequently executed ,6.$ '&2,$ !"#
  • $ (+,6$ D6.$ +*;&7),6'$ ?*)')-+,.Y-.?F,.-/$ +-+*5X.2$ +-/$ .*)')-+,.2$ &-.$ /$ 0&7E 2);-$ .F,.-2)&-$ G5$ 82)-;$ Z>[>Z$ %6+)-29$ :.$ +228'.$ ,6+,$ .+%6$ .7,)&-$ 6&4-$ Sign Extension Elimination )-2,78%,)&-$ 6+2$ ,67..$ 0*+;23$ ZQ?3$ >?J3$ +-/$ TWWT3$ ,&$ )-/)%+,.$ ,6+,$ ,6.$ )-2,78%,)&-$ 6+2$ G..-$ ,7+1.72./$ 0&7$ .+%6$ %6.%I9$ :.$ -&,.$ 7),6'$ 6.7.$ ,6+,$ UEG),$ +-/$ !]EG),$ 2);-$ .F,.-2)&-2$ +7.$ +*2&$ .*)')-+,./$ The algorithm EliminateOneExtend analyzes and eliminates one sign extension by using UD/DU chains. +*;&E G+2./$&-$,6.$2+'.$+*;&7),6'3$+*,6&8;6$4.$/.2%7)G.$,6.$+*;&7),6'$ &-*5$0&7$.*)')-+,)-;$LKEG),$2);-$.F,.-2)&-2$)-$,6)2$2.%,)&-9$ .1.75$ 01!+!,-*(%,(08*(,'<!"#@$^$ -/./3$ )-),)+*)X.$+**$0*+;2$<ZQ?3>?J3TWWT@$0&7$+**$)-2,78%,)&-2_$ +2.$&0$ 7.V8)7./$P$JT`Q?_$ .*)')E [a$82.$>ZE%6+)-$a[$ 0&7$<$$!$+**$)-2,78%,)&-2$,6+,$82.$,6.$/.2,)-+,)&-$&(.7+-/$&0$!"#@^$ *)')E 7.V8)7./$P$T-+*5X.ZQ?<!"#3$$3$DWZ?@_$ )0$<7.V8)7./@$G7.+I_$ b$ &-$+,$ )0$<7.V8)7./@^$ +,@$+,$ [a$82.$Z>E%6+)-$a[$ 0&7$<$$!$+**$)-2,78%,)&-2$,6+,$/.0)-.$,6.$2&87%.$&(.7+-/$&0$!"#@^$ $2);-$ 7.V8)7./$P$T-+*5X.>?J<$@_$ ./$ +2$ )0$<7.V8)7./@$G7.+I_$ b$ b$ )0$<c7.V8)7./@$.*)')-+,.$?dD_$ b$ ,$ 07.E G&,6$ R-$(7)-%)(*.3$+$2);-$.F,.-2)&-$%+-$G.$.*)')-+,./$)0$),2$2&87%.$&(.7E
  • Handling of Array Subscripts
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