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We focus on semantic analysis: compute a tight bound on the max and min number of iterations for every block consider different path frequencies inside loops avoid path enumerationNiJN1 BOutlinehGoal Loop bounds Block bounds Complexity and related work Testing environment Results Concluding remarkshi    d"System s overview JavaWhole program analysis. Variable type based analysis to resolve polymorphism. We consider only local integer variables for the loop analysis. Our block iterations bounding technique is language independent.:N@@  A'"System s overview ePartial abstract interpretation\We perform a limited abstract interpretation pass over linear code. We discover some false paths (not containing cycles). We gather information on possible variables values.D7 6 4Partial abstract interpretation Partial abstract interpretation "System s overview f Loop boundsBounds on the loop header computed similarly to C. Healy [RTAS 98]. We introduce noncontiguous sets of integers to easily handle equality operators. Iteration branch: a block where the conditional jump could be responsible for a loop exit. For each edge e and iteration branch ib we compute the possible number of iterations.GCR  J $$.((,,.+ Loop boundsThe bounds on the iterations of the header are safe for the whole loop. But: some parts of the loop could be executed less frequently:&H>,G:"System s overview iBasic block iterations^The number of iterations of a block is not a local property (based on immediate predecessors).&_'5 Basic block iterations^The number of iterations of a block is not a local property (based on immediate predecessors).&_'5!Basic block iterations^The number of iterations of a block is not a local property (based on immediate predecessors).&_'5Basic block iterations^The number of iterations of a block is not a local property (based on immediate predecessors).&_'5gStructural analysisPowerful interval analysis. Recognizes semantic constructs. Useful when the source code is not available. Iteratively matches the blocks with predefined patterns.0<.8  "Structural analysisPowerful interval analysis. Recognizes semantic constructs. Useful when the source code is not available. Iteratively matches the blocks with predefined patterns.0<.8  Structural analysisStatic patterns:zBlock iterationsBlock iterations are computed using the CFG root and the iteration branches. The header and the type of the biggest semantic region that includes all the predecessors of a node determine its number of iterations. Complete algorithm in the paper.`Q  R , Example #Example $Example W Related workAutomatically detected value-dependent constraints [Healy, RTAS 99]: per block bounds requires path enumeration (in the loop body) We propagate the header bounds to the blocks in quadratic time: Structural analysis: O(B2) Loop bounds: O(B) Block bounds: O(B)xE>A@E>@ &#Evaluation: hardware-level analysis$$$qThe semantic analysis is platform independent. Evaluation: Pentium III on Linux. We approximate the effects of caches and pipelines: we assume that the effects of an instruction fade over time. caches and pipelines are analyzed locally. Possible sources of inaccuracies: cache misses and pipeline stalls but not the number of iterations of an instruction (conservative)h"cQ4=+  !;  >}B% Evaluation $Base: the bounds on the iterations of the loop header are used for the whole loop. 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Co., Ltd.     hnamd` Arial&Monotype Typography  \ block bounds4    00O  4,H___PPT10( f___PPT9H@f___PPTMac11@8   hnamd` Arial&Monotype Typography  \namdTTahoma Microsoft Corp.  \namdTTahoma Microsoft Corp.    hnamd` Arial&Monotype Typography  {instruction duration analysisB    h"   0@; b=0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  8WCET^   6Ԕ|2^   6Ԕ^   6Ԕz ^  6Ԕ  ^ @ 6Ԕ< < ^ @ 6Ԕ< b < H  0޽h ?o       ̙33h`___PPT10@.p^+D' P= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D!' =4@BBBB%(D' =,54*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D!' =4@BBBB%(D' =,54ff*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*+} r ( D{313 l  C C0   l  C E<  H  0޽h ? ̙33___PPT10u.px+D=' = @B +C (r 33 W2( CCCC     <vC0 E 0___PPT106___PPT9H___PPT2001$GB___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]C   <+ a 0___PPT106___PPT9H___PPT2001$GB___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]C   <[N  0___PPT106___PPT9H___PPT2001$GB___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]C   < N`  0___PPT106___PPT9H___PPT2001$GB___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]C   <PN p $,0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  :[50]C   <mN +p $,0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  :[50]C   <P-C @ $,0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[100]Cl   C 00   l   C P<      s *gp` "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 e2   0P'A  0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  5Ae2   0I  0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  5BR2   s *0 UE R2   s *UE X  @ 0x X   0"x X   0 xS X  @ 0 "xS w   <NE0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[101]CR2   s *  p"   HZGH=I x p"  @ HGckHIjx R2   s *P P @@p   HGHI UP u   <0@P pm0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  9[1]C   <O  $,0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  ;[100]CB   6D|  ,$@,B   6D| @ ,$@,B   6D| @` ,$@,B   6D| p ,$D ,H   0޽h ?                       ̙33___PPT10b.px{+"DJ' P= @B D' = @BA?%,( < +O%,( < +D< ' =%(D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(++0+  ++0+  ++0+  ++0+  +\. r %%d$(  m  s *ʤ 0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  CSemantic analysisr  S ʤ0   ~"  0Ѥb0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  Nbytecode   "  0֤ 0___PPT106___PPT9B___PPTMac11   hnamd` Arial&Monotype Typography  c annotated asm   002B 4,H___PPT10( f___PPT9H@f___PPTMac11@8   hnamd` Arial&Monotype Typography  \namdTTahoma Microsoft Corp.  \namdTTahoma Microsoft Corp.    hnamd` Arial&Monotype Typography  }partial abstract interpretationB       0@ff2z 4,H___PPT10( f___PPT9H@f___PPTMac11@8   hnamd` Arial&Monotype Typography  \namdTTahoma Microsoft Corp.  \namdTTahoma Microsoft Corp.    hnamd` Arial&Monotype Typography  ploop header boundsB    02, 0(@___PPT10 V___PPT980z___PPTMac11TL   hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. 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