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S  6Du ``  >*  6z `   @*  A޽h ?Eighty Three:Users:dsrogers:Files:Workspace:2004 Retreat:white_slide.bmp 33 $Blank PresentationA  0 (     6P+ p@  T Click to edit Master title style! !  04 ` `    W#Click to edit Master subtitle style$ $  A޽h ?Eighty Three:Users:dsrogers:Files:Workspace:2004 Retreat:orange_title.bmp 33 0 zr (    0Z P    P*    0lZ     R*  d  c $ ?    0LY  @  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  6f `P   P*    6Tk `   R*  H  0޽h ? ̙33  $(  r  S ,9 p@  r  S 9 ` `    H  0޽h ? 33  0(  x  c $   x  c $p  H  0޽h ? 33y___PPT10Y+D=' = @B +  ,0(  ,x , c $   x , c $0PpP   H , 0޽h ? 33U   p2(M (  (x ( c $     ( < ; front end  2 ( <t 0 6code" ( <G 4IR ( <@  4CG ( < p  ? Search Engine ( <| 0  ? Loop Analyzer2 ( < 6codeL ( c $@ @L ( c $@0 @L ( c $`` L  ( c $@@d "( <ZGrHIrP L #( c $L $( c $@G@ %( < H CDriver generatorL &( c $  " '( <w @testing driverL (( c $ ,( <   Iinfo of tuning parameters -( 0 H `   Atuning parametersd .(@ <ZGHI  2( 0`4 3+ 2H ( 0޽h ?@ ((( (((((((( ((("(( (#( (($((%(&(%('((( ((.( 33  `t0(  tx t c $޳   x t c $p߳0P0P   H t 0޽h ? 33  P#'(  X  0@p0X  0p X  0 F  S p F  S pw F  S  X  0 X  0pF  S pw  0  NX20 2ai  0D  NX30 2ai  0 P0  NX10 2ai  0ԟ  `Xc0 2ai   00 `A {Basic idea of Simplex Method in 2D: To find maximum value of f(x) in a 2-dim search space The simplex consists X1, X2, X3. suppose f(X1) <= f(X2)<=f(X3) In each step, we can find Xc which is the centroid of X2 and X3, replace X1 with Xr which is the reflection of X1 through Xc.$ 2 2saia i ai ai a $i$(a(,i,0a04i48a8  l S ЖP    H l 0޽h ? 334  t(  r  S ,GP   r  S G  H  C A it2^0H  0޽h ? 33>  ~(  x  c $\9P   x  c $:  F  C A p4H  0޽h ? 33@  p(  x  c $p3P   x  c $4  H  C A p4xH  0޽h ? 33@  `(  x  c $P   x  c $`  H  C Appc}.H  0޽h ? 33   P(  r  S  `     0P  0 v cip2 = C[i + 2]; cip3 = C[i + 3]; cip4 = C[i + 4]; cip5 = C[i + 5]; cip6 = C[i + 6]; cip7 = C[i + 7]; bjp0 = B[j]; bjp1 = B[j+1]; bjp2 = B[j+2]; bjp3 = B[j+3]; bjp4 = B[j+4]; bjp5 = B[j+5]; cip0 += (A[t0]) * bjp0; & & .. C[i+6] = cip6; C[i+7] = cip7; } for (; j <= rosemin(N-1,_var_0+112); j++) { C[i] += (alpha * A[j * M + i]) * B[j]; C[i+1] += (alpha * A[j * M + i+1]) * B[j]; & & . C[i+7] += (alpha * A[j * M + i+7]) * B[j]; } } for (; i <= rosemin((M-1),(_var_1 + 112)); i++) { for (j = _var_0; j <= rosemin((N + -1),(_var_0 + 112)); j++) { C[i] += (alpha * A[(j * M + i)]) * B[j]; } } } } } ,XPZ tfj )H  0޽h ? 3380___PPT10.e" 0 /'(  X C    ' S o @   1We are trying to extend the idea of ATLAS, which performs empirical optimization for algorithms that are known ahead of time, to include optimization of arbitrary code segments. Among other things, the ROSE project from Lawrence Livermore National Lab provides a source-to-source code transformation tool that can produce blocked and unrolled versions of the input code (currently supporting only C). We have developed a test infrastructure that automatically generates a timing driver for the optimized routine based on a simple description of the arguments.tT3)eJsZH  0޽h ? 3380___PPT10.JVqb[ 0 k(  X C     S @ @   mYThis describes the basic operation of the simplex method and how the points are selected.H  0޽h ? 3380___PPT10.SVqۦf 0 v(  X C     S ( @   xIn the previous slides we were dealing with only two parameters, but now we consider the search space for ATLAS, which contains 8 dimensions. ATLAS performs an orthogonal search (optimizing one dimension at a time), but we are interested in applying the simplex method to this search problem. To keep the search time reasonable, we define constraints for each parameter. Note that we are still using the ATLAS code generator -- we have only replaced the search component of the system.t >\7H  0޽h ? 3380___PPT10.TVq^ 0 n(  X C     S  @   pThis graph compares the performance of the code generated by ATLAS versus the code generated using the simplex method.  ATLAS cgws (cgws == code generator with search) represents the original ATLAS search method. We show two simplex variations here. One has the block size bounded at 64 and the other at 32. The larger block size performs better, but requires a longer search time, even compared to the original ATLAS search.  mdel is a model-based technique developed at Cornell.]3H  0޽h ? 3380___PPT10.VVqE^ 0 n(  X C     S  @   pThis graph compares the performance of the code generated by ATLAS versus the code generated using the simplex method.  ATLAS cgws (cgws == code generator with search) represents the original ATLAS search method. We show two simplex variations here. One has the block size bounded at 64 and the other at 32. The larger block size performs better, but requires a longer search time, even compared to the original ATLAS search.  mdel is a model-based technique developed at Cornell.]3H  0޽h ? 3380___PPT10.VVqE^ 0 n(  X C     S  @   pThis graph compares the performance of the code generated by ATLAS versus the code generated using the simplex method.  ATLAS cgws (cgws == code generator with search) represents the original ATLAS search method. We show two simplex variations here. One has the block size bounded at 64 and the other at 32. The larger block size performs better, but requires a longer search time, even compared to the original ATLAS search.  mdel is a model-based technique developed at Cornell.]3H  0޽h ? 3380___PPT10.VVqE^ 0 n(  X C     S ] @   pThis graph compares the performance of the code generated by ATLAS versus the code generated using the simplex method.  ATLAS cgws (cgws == code generator with search) represents the original ATLAS search method. We show two simplex variations here. One has the block size bounded at 64 and the other at 32. The larger block size performs better, but requires a longer search time, even compared to the original ATLAS search.  mdel is a model-based technique developed at Cornell.]3H  0޽h ? 3380___PPT10.VVqE^ 0  n(  X C    ] S ] @  ] pThis graph compares the performance of the code generated by ATLAS versus the code generated using the simplex method.  ATLAS cgws (cgws == code generator with search) represents the original ATLAS search method. We show two simplex variations here. One has the block size bounded at 64 and the other at 32. The larger block size performs better, but requires a longer search time, even compared to the original ATLAS search.  mdel is a model-based technique developed at Cornell.]3H  0޽h ? 3380___PPT10.VVqE^ 0 0n(  X C    ] S ] @  ] pThis graph compares the performance of the code generated by ATLAS versus the code generated using the simplex method.  ATLAS cgws (cgws == code generator with search) represents the original ATLAS search method. We show two simplex variations here. One has the block size bounded at 64 and the other at 32. The larger block size performs better, but requires a longer search time, even compared to the original ATLAS search.  mdel is a model-based technique developed at Cornell.]3H  0޽h ? 3380___PPT10.VVqE^ 0 Pn(  X C    ] S 8] @  ] pThis graph compares the performance of the code generated by ATLAS versus the code generated using the simplex method.  ATLAS cgws (cgws == code generator with search) represents the original ATLAS search method. We show two simplex variations here. One has the block size bounded at 64 and the other at 32. The larger block size performs better, but requires a longer search time, even compared to the original ATLAS search.  mdel is a model-based technique developed at Cornell.]3H  0޽h ? 3380___PPT10.VVqE^ 0 @n(  X C    ] S *] @  ] pThis graph compares the performance of the code generated by ATLAS versus the code generated using the simplex method.  ATLAS cgws (cgws == code generator with search) represents the original ATLAS search method. We show two simplex variations here. One has the block size bounded at 64 and the other at 32. The larger block size performs better, but requires a longer search time, even compared to the original ATLAS search.  mdel is a model-based technique developed at Cornell.]3H  0޽h ? 3380___PPT10.VVqEr0!S+^4 :8@~W,IP.J6N$Kaf2knpszvhְ<n|:1p=y.v$79"( / 0DTimesNew RoH7$\4t\ )0tY 0 DTimes New Roman\4t\ )0tY 0 DArialNew Roman\4Oh+'0Q hp    (Generic Code Optimizationi David RogersOptaviShirley Moorept17rMicrosoft PowerPointtio@b@ @%gGPg  R('& &&#TNPP,2OMi & TNPP &&TNPP     'A x(xKʦ 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