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We discover some false paths (not containing cycles). We gather information on possible variables values. D76 40Loop Iteration BoundsBounds on the loop header computed similarly to C. Healy [RTAS 98]. Each loop is handled in isolation by analyzing the behavior of induction variables. we consider integer local variables we handle loops with several induction variables and multiple exit points computes the minimal and maximal number of iterations for each loop headerbDT$ IJPD U2Loop Header IterationsThe bounds on the iterations of the header are safe for the whole loop. But: some parts of the loop could be executed less frequently:&H>,G:7Block Iterations HExample 8!Contributions (Semantic Analysis)We compute bounds on the iterations of basic blocks in quadratic time: Structural analysis: O(B2) Loop bounds: O(B) Block bounds: O(B) Related work Automatically detected value-dependent constraints [Healy, RTAS 99]: Abstract interpretation based approachesxGA nF   n,Q)9Outline`Goal and thesis Semantic analysis Hardware-level analysis Environment Results Concluding remarksla    !?:Instruction Duration EstimationGoal: compute the duration of the single instructions The maximum number of iteration for each instruction is known The duration depends on the context Limited computational context: We assume that the effects on the pipeline and caches of an instruction fade over time. VZYZZ/= ,mJY<Partial Traces =WCET EstimationFor every partial trace: CPU behavior simulation (cycle precise) duration according to the context We account for all the incoming partial traces (contexts) according to their iteration counts Block duration = " instruction durations WCET = longest path`J'  !  I Data CachesPartial traces are too short to gather enough information on data caches Data caches are not simulated but estimated using run-time statistics The average frequency of data cache misses is measured with a set of test runs of the program ZZIE /'>9JUPStructure: Separated Approach  > ApproximationWe approximate the duration of single instructions. We do not approximate the number of times an instruction is executed. Inaccuracies are only due to cache and pipeline effects. No severe WCET underestimations are possible. N4F9 -, D!Contributions (HW-level Analysis)Partial traces evaluation O(B) analyze the instructions in their context approximates the effects of instructions over time includes run-time data for the analysis of data caches Related work abstract interpretation based data flow analyses ZZ Z2ZZ$ * 3  6  $   $$ (( ,,$P8U(3?Outline`Goal and thesis Semantic analysis Hardware-level analysis Environment Results Concluding remarksza     $$!?@ EnvironmentJava ahead-of-time bytecode to native compiler Linux Intel Pentium Pro family Semantic analysis: language independent Hardware-level analysis: architecture independent P/( 26M'1JOutline`Goal and thesis Semantic analysis Hardware-level analysis Environment Results Concluding remarks~a     $$!? N EvaluationIt is not possible to test the whole input space to determine the WCET experimentally. small applications: known algorithm, the WCET can be forced at run time big applications: several runs with random inputNW6  ,WeB.Results  Small Kernels C@Results  Application Benchmarks KOutline`Goal and thesis Semantic analysis Hardware-level analysis Environment Results Concluding remarksa     $$((!?O Conclusions=Semantic analysis fast partial abstract interpretation pass scalable block iterations bounding algorithm taking into consideration different path frequencies inside loop bodies no restrictions on the analyzed code Hardware-level analysis instruction duration analyzed in the execution context architecture independentvP*u% 7b;" lN/H[\   !"#&'(PIsx,, ; > w ze{HH(d"h   83 ` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@(@|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> (    6Вy 0  T Click to edit Master title style! !  0y <  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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H $ 0޽h ?$ ̙33___PPT10u.aqV+D=' ϐ= @B +}   0( c noatni 0l 0 C  0   l 0 C  <  H 0 0޽h ? ̙33___PPT10u.aqLM+D=' = @B +D   !44!82( ! 8l 8 C  0    8 <0 0 E 0___PPT106___PPT9H___PPT2001$FB___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]C 8 <p  a 0___PPT106___PPT9H___PPT2001$FB___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]C 8 <   0___PPT106___PPT9H___PPT2001$FB___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]C 8 < ` 0___PPT106___PPT9H___PPT2001$FB___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]C 8 <  p $,0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  :[50]C  8 <  +p $,0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  :[50]C  8 <P  @ $,0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[100]C  8 <p  <     8 s *` p` "p___PPT10PH___PPT9___PPTMac11|t (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  yIfor(int i=0; i<100; i++) { if (i < 50) { A; } else { B; } }JCCC C CCCC C t k2  8 6 8c  0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  5Ak2 8 6 8c  0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  5BX2 8 08c0 UE X2 8 08cUE ^ 8@ 68cx ^ 8 68c"x ^ 8 68c xK ^ 8@ 68c "xK w 8 <0 E0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]CX2 8 08c  v" 8 NZGDHIN8c x( v" 8@ NGjHsI8cx X2 8 08cP P @@v 8 NGHI8c MH u 8 < P pm0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  9[1]C 8 < ` Y $,0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[100]CB 8 6D8c  ,$@,B 8 6D8c @ ,$@,B 8 6D8c0 00 ,$@,B  8 6D8c p ,$D ,H 8 0޽h ?8 88888 888888888888888 ̙33___PPT10b.aqvCZ+Y <DJ' = @B D' = @BA?%,( < +O%,( < +D< ' =%(D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(++0+8 ++0+ 8 ++0+ 8 ++0+8 +  t(  tl t C  0   R t s * P X t 08c` X t 08c `  t 0  <TLX___PPT1080___PPT9h`V___PPTMac110(   hnamd` Arial&Monotype Typography   cBlock iterations are computed using the CFG root and the iteration branches. 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R *  s *̙PP R )  s *P` R (  s * l   C  0   =   s * @   ___PPT10ph    ___PPT9     ___PPTMac11   (namd Monaco  (namd Monaco        !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnoprstuvwxyz{|}~(namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  (namd Monaco  Cyvoid foo() { int i,j; for(i=0; i<100; i++) { if (i < 50) { for(j=0; j<10; j++) ; } } }zC CC C CC CC C $C$(C(,C,0C0 2   < 8c"A V 0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  > 2   <0 8c" w, 0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  > l2   68c"wr   <8c" "   NG,HTI8c"? r   <8c"r  @ <8c"~9 l2   68c"*?l2   68c"7L r  @ <8c"r   <8c" ~9 "   NGH"I8c"LG l2   68c"(*?=r   <8c"El2   68c" ^"   6Ԕ`` ^"   6Ԕ  u   <7 @0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  9[1]Cw   <0> Pg0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]Cw !  <D W0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[550]Cw "  <@M  y 0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[100]Cv #  <N "0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  :[50]Cv" %  NGQHP2I4 8cL".w &  < X  P 0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[500]Cu '  <_  0-0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  9[1]CH   0޽h ?                              %  ̙33___PPT10u.hqƐ+D=' ϐ= @B +  x(  xl x C  0    x c ` 0e0e "`<  H x 0޽h ? ̙33___PPT10u.aq l+D=' = @B +y   |$(  |r | S p 0   r | S  4~  H | 0޽h ? ̙33___PPT10e+D=' = @B +  0( T@@WC l  C A 0   R  s *a    <C  <  H  0޽h ? ̙33___PPT10u.aqK+D=' = @B ++  W O 0_ ( Fs   c $A  ??8  $ 8l  C e0   @  0m <M vthe last n instructions before the instruction i on a given trace n is determined experimentally (50-100 instructions)Nw %  4f  0Zff"@ 0 0 `  s *ff"0 0  `  s *"0 f  0Zff"`   s *ff"p` f   0Zff"` P f   0Z"P@pf   0Z"pP@` f  0Z"0 `  s *ff"0 f  0Zff"0 q  0pzf" 0 0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  3iX  0X @ 0X @ 0O ? 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