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Topic 5a Partial Redundancy Elimination and SSA Form

Topic 5a Partial Redundancy Elimination and SSA Form. References. Robert Kennedy, Sun Chan, Shin-ming Liu, Raymond Lo, Pend Tu, Fred Chow. Partial redundancy elimination in SSA Form . ACM Trans. On Programming Languages and Systems, 21(3), May 1999: 627-676.

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Topic 5a Partial Redundancy Elimination and SSA Form

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  1. Topic 5aPartial Redundancy Elimination and SSA Form \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  2. References • Robert Kennedy, Sun Chan, Shin-ming Liu, Raymond Lo, Pend Tu, Fred Chow. Partial redundancy elimination in SSA Form. ACM Trans. On Programming Languages and Systems, 21(3), May 1999: 627-676. • Drechsler K. and Stadel M. A variation of Knoop, Ruthing, and Steffen’s lazy code motion. SIGPLAN Notices, 28(5), May, 1993: 29-38. • Keith Cooper, Linda Torczon. Engineering a compiler. 2004 \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  3. Outline • Partial Redundancy Elimination (PRE) • SSAPRE (a short summary) \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  4. C++ Fortran C Front end • Source to IR (Scanner →Parser →RTL →WHIRL) fe90 gfec gfecc • VHO(Very High WHIRL Optimizer) • Standalone Inliner • W2C/W2F Middle end Very High WHIRL • IPA (inter-procedural analysis & opt) • LNO (Loop unrolling/fission/fusion/tiling/peeling etc) • PREOPT (point-to analysis etc) Machine Model High WHIRL • WOPT • - SSAPRE (Partial Redundancy Elimination) • - VNFRE (Value numbering based full redundancy elim.) • RVI-1 (Register Variable Identification) Middle WHIRL Low WHIRL • RVI-2 Back end • Some peephole opt Very Low WHIRL • Cflow (control flow opt) • EBO (extended block opt.) • PQS (predicate query system) • Loop Opt (Unrolling + SWP) • GCM(global code motion), HB sched(hyperblk schedule) • GRA/LRA(global/local register alloc) CGIR Asm file KCC Compiler Infrastructure \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  5. Important Observation • An operand of a  function is regarded as occurring at the end of its corresponding predecessor block. • The result of a function is regarded as occurring at the beginning of the block that contains it. \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  6. Partial Redundancy Elimination Is the program in SSA form before and after PRE? tx*y a t a x*y B1 tx*y B2 X*y is partially redundant here b x*y b t B3 X*y is made redundant here \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  7. Problem Formulation for PRE • For an expression, identify its partially redundant occurrences • Safely insert occurrences (to new temporaries) at some points • Delete the original partially (now fully) redundant occurrences. Replace them by loads from a temporary variable. \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  8. PRE Basics • Availability: An expression, say, x*y, is available at a program point p if • EVERY path from entry to p evaluates the expression before reaching p • And there are no assignments to x or y after the (last) evaluation but before p (on all paths). • Availability implies full redundancy. \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  9. PRE Basics (Cont.) • Partial availability: An expression, say, x*y, is partially available at a program point p if • SOME paths from entry to p evaluates the expression before reaching p • And there are no assignments to x or y after the (last) such evaluation but before p. • Partial availability implies partial redundancy. \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  10. B1 a x*y B3 b x*y PRE Basics (Cont.) • Anticipatability: An expression e is anticipatable ( “down-safe”) at a program point p if it appears (without redefinition) along ALL paths from • p to an exit of the program X*y is anticipatable here B2 \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  11. Safe Placement - Safe insertion: If an inserted computation occurs at a point where the computation is anticipated. - Unsafe insertion: means that some original path in the program did not contain this computation. • May increase the execution time of the program • May cause exceptions \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  12. Safe Placement: Example x*y x*y This is called an “critical edge”. Allowable if we can insert computations on an edge. Otherwise, need split Safe Not safe \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  13. Optimal Placement (Cont’d) • Computationally optimal • If no other safe placement can result in fewer occurrences of the computation along any path from entry to exit in the program. \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  14. Optimal Placement (cont’d) • Lifetime optimal • Minimize the lifetimes of the introduced temporaries. • Intuition: delay an expression to the latest point (Lazy Code Motion [KnoopEtal92, DrechslerStadel93]) \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  15. Outline • Partial redundancy elimination (PRE) • SSAPRE (a short summary) \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  16. SSAPRE \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  17. SSAPRE: Motivation • Traditional data flow analysis based on bit-vectors do not interface well with SSA representation \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  18. B1 a x*y B2 b x*y B3 Traditional Partial Redundancy Elimination Before PRE SSA form tx*y a t After PRE B1 tx*y B2 Not SSA form! b t B3 \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  19. SSAPRE: Motivation (Cont.) • Traditional PRE needs a postpass transform to turn the results into SSA form again. • SSA is based on variables, not on expressions \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  20. SSAPRE: Motivation (Cont.) • Representative occurrence • Given a partially redundant occurrence E0, we define the representative occurrence for E0 as the nearest to E0 among all occurrences that dominate E0. • Unique and well-defined \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  21. E E E E Control flow edge E =(E, E, ) Redundancy edge E E E E Factored FRG (Factored Redundancy Graph) Without factoring \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  22. t0 x*y t1 x*y t2(t0, t1 , t3) t2 t2 FRG (Factored Redundancy Graph) E E E =(E, E, ) E E Note: This is in SSA form Assume E=x*y \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  23. Observation • Every use-def edge of the temporary corresponds directly to a redundancy edge for the expression. \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  24. Intuition for SSAPRE • Construct FRG for each expression E • Refine redundant edges to form the use-def relation for each expression E’s temporary • Transform the program • For a definition, replace with tE • For a use, replace with t • Sometimes need also insert an expression \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt

  25. An Example a1 t1 a1+ b1 B1 a1 B1 t2(t4 , t1) a2(a4 , a1) a2(a4 , a1) B2 B2 t2 a3 t3a3+ b1 a2+b a3 B3 a4(a2, a3) a4+b t4(t2, t3)a4(a2, a3) t4 B4 B4 B5 exit \course\cpeg421-08s\Topic-5a.ppt\course\cpeg421-07s\Topic-7b.ppt exit

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