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Control Localization in Domain Specific Translation

Control Localization in Domain Specific Translation. Ted J. Biggerstaff tbiggerstaff@austin.rr.com. Overriding Problem: Antagonistic Goals. High level operators and operands provide programming leverage & variations E.g., ( image  neighborhood) convolution

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Control Localization in Domain Specific Translation

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  1. Control Localization in Domain Specific Translation Ted J. Biggerstaff tbiggerstaff@austin.rr.com

  2. Overriding Problem: Antagonistic Goals • High level operators and operands provide programming leverage & variations • E.g., (image  neighborhood) convolution • But fracture and de-localize code pieces • b=((a  s)2 + (a  s’)2 )1/2 • Needed optimizations: code sharing, re-org. & re-weaving • Conventional Optimization approaches induce large search spaces (EXPLOSION)

  3. x Constraint x Constraint Propagation NP Complete Reuse Library Alternative Refinements of Program Refine to

  4. Existing Explosion Control: DS Reductionism • Implicit Phases based on Distinct DSLs • Mutually Exclusive DSL Operators & Operands • Inter-Phase Optimization • Metaprogram = {Refine DSL; Optimize Refined DSL} • Result: Group Rules by Phase • One large search space to several small ones

  5. (p, q : a i+p , j+q) (i, j : a i , j) Image a (p, q (sp , q * a i+p , j+q)) * s-1,-1 * s-1,0 b[i,j] + * s-1,1 * s1,1 If hanging then b[i,j]=0 else sum of products loop b[i,j]=0 Large Grain Data & Operators Imply Control b=(a  s)

  6. DSL for Sobel Edge Detection b=[(a  s)2 + (a  s’)2]1/2 a b

  7. Large Grain Extended Expressions (p, q (a i+p , j+q * sp , q)) (p, q (a v+p , w+q * s’p , q)) b=((a  s)2 + (a  s’)2 )1/2 (d,e: a d,e) (i, j : a i , j) (v,w: a v , w)

  8.  Weave   Explosion Control • DSL-> DSL translation phases • DS optimizations • Specialized metaprograms (Control Localization)

  9. Localizing Implied Control b=((a  s)2 + (a  s’)2 )1/2 b=(((i, j : a i , j)  s)2 + ((v, w : a v , w)  s’)2 )1/2 b=(((i, j : (p,q:ai+p , j+q * sp,q))2) +((v, w:(p,q:a v+p , q+w*s’p,q))2))1/2

  10. Localizing Implied Control b=(((i, j : (p,q:ai+p , j+q * sp,q))2) +((v, w:(p,q:a v+p , w+q*s’p, q))2))1/2 b=((i, j : ((p,q: ai+p , j+q * sp,q))2) +(v, w:((p,q: a v+p , w+q*s’p, q))2))1/2 b=(i, j : (((p,q:ai , j * si+p,j+q))2) + (((p,q: a i+p , j+q*s’p, q))2))1/2

  11. Localizing Implied Control b=(i, j : (((p,q:ai , j * si+p,j+q))2) + (((p,q: a i+p , j+q*s’p, q))2))1/2 b=i, j : ((((p,q:ai , j * si+p,j+q))2) +(((p,q: a i+p , j+q*s’p, q))2))1/2 (d, e:bd , e)=i, j : ((((p,q:ai , j*si+p,j+q))2) + (((p,q: a i+p , j+q*s’p, q))2))1/2

  12. Localizing Implied Control (d, e:bd , e) =i, j : ((((p,q:ai , j*si+p,j+q))2) + (((p,q: a i+p , j+q*s’p, q))2))1/2 (i, j : (b i, j=(((p,q:ai , j*si+p,j+q))2) + (((p,q: a i+p , j+q*s’p, q))2))1/2)

  13.  Weave   Explosion Control • DSL-> DSL translation phases • DS optimizations • Specialized metaprograms (Control Localization) • Group rules by object & phase • Use domain knowledge

  14. Explicit Entities & Phases

  15. Example Loop Opt. Transform 

  16. Example (Idealized) AST Transformation b=((a  s)2 + (a  s’)2 )1/2  b=(((i, j : a i , j)  s)2 + (a s’)2 )1/2

  17. Example (Actual) AST Transformation b=((a  s)2 + (a  s’)2 )1/2  b=((( idx2139, idx2145: bwpixel2136)  s)2 + (a s’)2 )1/2 Wherebwpixel2136 =a idx2139, idx2145

  18. CLOS Object Property List  (leaf a (tags (itype image))) b=((( idx2139, idx2145: bwpixel2136)  s)2 + (a s’)2 )1/2 (leaf bwpixel2136 (tags (_q (_forall (idx2139 idx2145) (_suchthat (_member idx2139 (_range 0 (- m 1))) (_member idx2145 (_range 0 (- n 1))) (mappings (bwpixel2136) (a))))) (itype bwpixel))) Example (Implementation) AST Transformation b=((a  s)2 + (a  s’)2 )1/2

  19. Name, Phase, Location Example Loop Opt. Transform • Refine Image to BWPixel with loop shorthand tags (=> compositeleaf fusion2 image LHS RHS PreRoutine PostRoutine)

  20. Name, Phase, Location Example Loop Opt. Transform • Refine Image to BWPixel with loop shorthand tags (=> compositeleaf fusion2 image `$(pand $(por (leaf ?op) ?op)) …sub-pattern to get type … …sub-pattern to get dimensions of ?op…) LHS RHS PreRoutine PostRoutine)

  21. Name, Phase, Location Example Loop Opt. Transform • Refine Image to BWPixel with loop shorthand tags (=> compositeleaf fusion2 image `$(pand $(por (leaf ?op) ?op)) ($(spanto ?pre (tags)) (tags $(spanto ?pretags (itype ?itype)) ?spaceover $(remain ?posttags))) …sub-pattern to get dimensions of ?op…) LHS RHS PreRoutine PostRoutine)

  22. Name, Phase, Location Example Loop Opt. Transform • Refine Image to BWPixel with loop shorthand tags • Enablecompositeleaf creates ?newleaf, ?idx1, ?idx2 (=> compositeleaf fusion2 image `$(pand $(por (leaf ?op) ?op)) ($(spanto ?pre (tags)) (tags $(spanto ?pretags (itype ?itype)) ?spaceover $(remain ?posttags))) …sub-pattern to get dimensions of ?op…) LHS RHS enablecompositeleaf nil) Pre &Post Routines

  23. RHS Rewrite Form `(leaf ?newleaf (tags (commasplice ?pretags) (_q (_forall (?idx1 ?idx2) (suchthat (_member ?idx1 (_range ?ilow ?ihigh)) (_member ?idx2 (_range ?jlow ?jhigh)) (mappings (?newleaf) (?op))))) (itype BWPixel) (commasplice ?posttags)))

  24. Name, Phase, Location Example Loop Opt. Transform • Refine Image to BWPixel with loop shorthand tags • Enablecompositeleaf creates ?newleaf, ?idx1, ?idx2 (=> compositeleaf fusion2 image `$(pand $(por (leaf ?op) ?op)) ($(spanto ?pre (tags)) (tags $(spanto ?pretags (itype ?itype)) ?spaceover $(remain ?posttags))) …sub-pattern to get dimensions of ?op…) LHS `(leaf ?newleaf (tags (commasplice ?pretags) (_q (_forall (?idx1 ?idx2) (suchthat (_member ?idx1 (_range ?ilow ?ihigh)) (_member ?idx2 (_range ?jlow ?jhigh)) (mappings (?newleaf) (?op))))) (itype BWPixel) (commasplice ?posttags))) RHS enablecompositeleaf nil) Pre &Post Routines

  25. Loop Control Phase Traversal You Are Here b=[(a  s)2 + (a  s’)2]1/2 Property List Behind The Scenes (leaf a (tags (itype image))) CLOS Object

  26. b=[(a  s)2 + (a  s’)2]1/2 Pattern Match Result `$(pand $(por (leaf ?op) ?op)) ($(spanto ?pre (tags)) (tags $(spanto ?pretags (itype ?itype)) ?spaceover $(remain ?posttags)))…) ?op { ?spaceover Behind The Scenes { { (leaf a (tags (itype image))) ?posttags ?pre ?itype ?pretags

  27. b=[(a  s)2 + (a  s’)2]1/2 Pattern Match Result Define enablecompositeleaf (at, bindings) {?idx1 = Create iterator; ?idx2 = Create iterator; ?newleaf = Create bwpixel; return extended bindings} ?idx1  idx2139 ?idx2  idx2145 ?newleaf  bwpixel2136 ?op { ?spaceover Behind The Scenes { { (leaf a (tags (itype image))) ?posttags ?pre ?itype ?pretags

  28. Rewrite Result b=[(bwpixel2136  s)2+ (a  s’)2]1/2 `(leaf ?newleaf (tags (commasplice ?pretags) (_q (_forall (?idx1 ?idx2) (suchthat (_member ?idx1 (_range ?ilow ?ihigh)) (_member ?idx2 (_range ?jlow ?jhigh)) (mappings (?newleaf) (?op))))) (itype BWPixel) (commasplice ?posttags))) (leaf bwpixel2136 (tags (_q (_forall (idx2139 idx2145) (_suchthat (_member idx2139 (_range 0 (- m 1))) (_member idx2145 (_range 0 (- n 1))) (mappings (bwpixel2136) (a))))) (itype bwpixel)))

  29. Bindings Before History After Transform Shown In Debugger

  30. Speculative Refinement • Dynamically build coordinated rules to express constraint set bwpixel2034  b idx2037, idx2043 idx2139  idx2037 idx2145  idx2043 bwpixel2987  bwpixel2136 bwpixel2136  a idx2037, idx2043

  31. Explosion Control • DSL-> DSL translation phases • DSL specific optimizations • Simplification & DS Optimizations • Key Point: DS Reductions Not Combinations • Localization • Separate Parts Woven into Computational Form • Group Rules by Object & Phase • Use Domain Knowledge • Architectural Shaping • Interdependent, Composed Parts Changed per Global Constraints

  32. References • Katz & Volper, Constraint Propagation in Software Libraries of Transformation Systems, IJSE&KE 2,3, 1992. • Biggerstaff, Fixing Some Transformation Problems, Proc. Of Automated Software Engineering, 1999. • Biggerstaff, A New Control Structure for Transformation-Based Generators, ICSR 2000. • Neighbors, Draco: A Method for Engineering Reusable Software Systems, inSoftware Reusability, 1989.

  33. The End

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